PREVIOUS SEMINAR PROGRAM

2024

9.12. - Isambard Goodbody (Univ. Glasgow): Strong Generation by Injectives
Abstract: Strong generation of a triangulated category is a notion which lets one encode notions of smoothness and dimension into the derived category of a ring or a scheme. There are many results along these lines beginning with Rouquier and, more recently, by Neeman. For example, the global dimension of a Noetherian ring is equal to the minimal generation time of the perfect complexes with respect to the regular module. For schemes we no longer have such a candidate generator, and a conjecture of Orlov asks one to consider all possible generators to extract the dimension. We take a different approach by taking our candidate generator to be all of the injectives. This project is a work in progress and there are still many unanswered questions.

2.12. - Kateřina Fuková (MFF UK): Multiplicative bases and commutative von Neumann regular algebras
Abstract: Let R be a semiartinian (von Neumann) regular ring with primitive factors artinian. The dimension sequence D of R was defined in order to capture the various skew-fields and dimensions occurring in the layers of the socle sequence of R. We will show that in the particular case when K is a field and R is a commutative semiartinian regular K-algebra of countable type, D determines the structure of R uniquely up to a K-algebra isomorphism. Our proof is constructive: given the sequence D, we construct the unique K-algebra R of countable type by a transfinite iterative construction from the base case of the K-algebra B(aleph_0,K) consisting of all eventually constant sequences in K^omega. As a corollary, we prove that each commutative semiartinian regular K-algebra of countable type has a conormed multiplicative basis. We also answer in the positive an old question of Eklof by showing the existence of strictly lambda-injective modules for all infinite cardinals lambda. Such modules exist over the K-algebra B(kappa,K) for each cardinal kappa > lambda.

11.11. - Isaac Bird (MFF UK): A non-monoidal homological spectrum
Abstract: I will introduce a construction which, by generalising the Homological spectrum of Balmer-Krause-Stevenson, provides a topological space parametrising certain thick subcategories of compact objects in an arbitrary compactly generated triangulated category. Through examples, I will relate this topological space to other non-monoidal analogues of the Balmer spectrum, given by Gratz-Stevenson, Krause, and Matsui. In the case of a big tensor-triangulated category, I will relate show how this space related to the Balmer spectrum. This talk is based on joint work with Jordan Williamson and Alexandra Zvonareva.

4.11. - Enrico Sabatini (Univ. Padova): Compactly generated t-structures of path algebras over commutative Noetherian rings
Abstract: The problem of characterising subcategories of the derived category of a commutative Noetherian ring has been studied extensively in the last thirty years. The most important results are the characterisation of localising subcategories in terms of subsets of Spec(R), the prime spectrum of the ring, due to A. Neeman in 1992, and the characterisation of compactly generated t-structures in terms of chains of these subsets, due to L. Alonso, A. Jeremías and M. Saorín in 2010. The first result was generalised by B. Antieau and G. Stevenson in 2016 to the derived category D(RQ) of representations of a quiver Q over a commutative Noetherian ring R. In particular, they proved that a characterisation of localising subcategories of D(RQ) in terms of functions from Spec(R) to a set Nc(Q), depending on Q, holds for any Dynkin quiver and commutative Noetherian ring. The aim of this project is to find the corresponding generalisation of the result concerning compactly generated t-structures. In this talk I will give an overview of the history of this project, introduce all the ingredients and show the results mentioned above. Finally, I will talk about the new results and the techniques that have been developed in order to solve the problem in this more general context.

21.10 - Simone Virili (UA Barcelona) A study of Sylvester rank functions via coherent functors
Abstract: Given a ring R, a Sylvester module rank function ρ on the category mod-R of finitely presented right R-modules is a real-valued function which is additive on coproducts, subadditive on right-exact sequences, and normalized by ρ(R)=1. Classically, they have been studied by P. Malcomson, A.H. Schofield and, in a slightly different context, by W. Crawley-Boevey while, more recently, they played an important role in A. Jaikin-Zapirain’s approach to the Atiyah and to the Lück approximation conjectures. In this talk I will start by observing that the rank functions on mod-R are in bijection with, suitably normalized, additive functions on the category of coherent functors Ab(R):=fp[R-mod,Ab]. Exploiting this connection I will extend and give new, simplified, proofs of several results of Schofield, Li, and Jaikin-Zapirain.

14.10 - Souvik Dey (MFF UK): On reducing homological dimensions
Abstract: The notion of reducing homological dimensions of finitely generated modules over commutative Noetherian rings has been recently introduced by Tokuji Araya and Olgur Celikbas, and traces its roots back to the notion of modules of reducible complexity by Petter Andreas Bergh. It was already shown by Bergh that modules of finite reducible complexity strictly contain the class of modules of finite complete intersection dimension. With the new notion of reducing homological dimensions, Araya and Celikbas showed that modules of finite reducing projective dimension satisfy a strong form of Auslander-Reiten conjecture, and also that semi-Gorenstein-projective modules of finite reducing Gorenstein dimension are Gorenstein projective. In this talk, I will try to motivate and convince why the definition of reducing dimensions are a natural generalization of standard homological dimensions, and discuss joint work with Olgur Celikbas, Toshinori Kobayashi and Hiroki Matsui on the finiteness of reducing projective dimension for the residue field of a local ring, and progress towards characterizing Gorenstein and complete intersection local rings via reducing homological dimensions.

7.10 - Leonid Positselski (IM CAS): Semiderived categories of modules, quasi-coherent sheaves, and contraherent cosheaves
Abstract: A semiderived category is constructed by mounting the conventional derived category on top of the coderived or contraderived category. This construction was originally invented in the context of semialgebras over coalgebras or corings and served the needs of the semi-infinite homological algebra theory. I will start with explaining this concept in the simpler context of a noncommutative ring homomorphism A --> R. Then I will pass to a morphism of schemes Y --> X and consider quasi-coherent sheaves and, time permitting, also contraherent cosheaves.

12.6 - Matthew Habermann (Univ. Hamburg): Homological Berglund-Hübsch-Henningson mirror symmetry for curve singularities
Abstract: Invertible polynomials are a class of hypersurface singularities which are defined in an elementary way from square matrices with non-negative integer coefficients. Berglund—Hübsch mirror symmetry posits that the polynomials defined by a matrix and its transpose should be mirror as Landau—Ginzburg models, and an extension of this idea due to Berglund and Henningson postulates that this equivalence should respect equivariant structures. In this algebraically orientated talk, I will begin by giving some background and context for the problem, and then explain of my recent work proving conjecture in the first non-trivial dimension; that of curves. They key input is detailed calculations in categories of graded matrix factorisations, as well as a model for the orbifold Fukaya--Seidel category in this context which takes inspiration from the crepant resolution conjecture.

20.5 - Pavel Čoupek (Michigan State Univ.): Ramification bounds via Breuil-Kisin and q-crystalline cohomology
Abstract: Let K be a finite extension of Q_p of ramification index e., and let X be a smooth proper scheme over the ring of integers of K. I will discuss how to obtain bounds on ramification for the mod p Galois representation arising from i-th étale cohomology of (geometric generic fiber of) X in terms of i, p and e. Key input in achieving this are various instances of prismatic cohomology of X: in general, one can use the Breuil-Kisin cohomology together with the Ainf-cohomology of X, and a series of conditions that control the Galois action on elements of the former inside the latter. When K/Q_p is unramified, one can similarly use q-crystalline cohomology to obtain slightly better bounds. (This last part is current work in progress.)

13.5 - Chris Lambie-Hanson (IM CAS, Prague): Whitehead's problem and condensed mathematics
Abstract: Whitehead's problem, which asks whether every Whitehead abelian group is a free abelian group, was a prominent open question in group theory in the mid-20th century. In 1974, Shelah proved that the problem is independent of ZFC, which was a surprising development and provided one of the first instances of a major problem coming from outside logic and set theory to be proven independent of ZFC. In recent years, Clausen and Scholze have introduced the framework of condensed mathematics as a setting in which to apply algebraic tools to the study of algebraic structures carrying topologies. Through some deep structural analysis of the category of condensed abelian groups, they showed that, when appropriately interpreted, Whitehead's problem is not independent in this setting: it is provable in ZFC that every abelian group that is Whitehead in the condensed category must be free. In this talk, we sketch a new, more concrete proof of Clausen and Scholze's result, in the process highlighting some connections between condensed mathematics and the theory of set-theoretic forcing. We will end by considering some variations on this question in the context of condensed or solid abelian groups. This is joint work with Jeffrey Bergfalk and Jan Šaroch.

6.5 - Sean Cox (VCU, Richmod, USA): Set-theoretic tools for approximation theory
Abstract: We demonstrate how set-theoretic elementary submodel techniques can be used to give relatively short proofs of many results, both old and new, in approximation theory. We also discuss our modest strengthening of some recent theorems of Cortes-Izurdiaga and Saroch.

22.4 - Álvaro Sánchez Campillo (Univ. Murcia): Abstract representation theory via coherent Auslander-Reiten diagrams
In this talk we explain a method to study representations of quivers over arbitrary stable \infty-categories in terms of Auslander-Reiten diagrams. Our techniques allow us to internally visualize (a significant piece of) the Auslander-Reiten quiver of the derived category of a hereditary finite-dimensional algebra inside much more general (\infty-)categories of representations, such as representations over arbitrary rings, schemes, dg algebras, or ring spectra. This is provided by an equivalence with a certain mesh subcategory of representations of the repetitive quiver, which we build inductively using abstract reflection functors. As an application we obtain that the automorphism group of the non-regular components of the Auslander-Reiten quiver acts on the \infty-category of representations over any stable \infty-category. When specialized to representations of trees over a field, this action gives an isomorphism with the derived Picard group as shown by Miyachi and Yekutieli.

15.4 - Nicola Carissimi (Univ. Lille): Day convolution product in the bicategory of Mackey pseudofunctors
Abstract: This talk aims to introduce the main objects and constructions in the theory of Mackey pseudofunctors, developed in order to provide an axiomatic framework to some classical phenomena in the representation theory of finite groups. It is frequent indeed in equivariant mathematics to associate an object M(G) to any finite group (or groupoid) G, and to have not only a restriction from M(G) to M(H) for every subgroup H < G, but also two isomorphic way to go the other way around, usually called induction and corestriction. Also, a base change (or "Mackey", in some contexts) formula holds true, and this categorical axiomatic framework allows us to deal with all this in a neat way. Then, it will be shown how a monoidal structure can be inferred on the universal bicategory for these pseudofunctors, allowing to define a Day convolution product. Monoids for this product will coincide with the adequate monoidal structure on a Mackey pseudofunctor, the so-called Green pseudofunctor structure.

8.4 - Leonid Positselski (IM CAS): Coderived and contraderived categories of CDG-modules
Abstract: The classical results of Jorgensen, Krause, Neeman, and Stovicek describe the full subcategories of compact objects in the categories of unbounded complexes of projective and injective modules over coherent rings. In this talk, I will explain how to extend these results to curved DG-modules over a CDG-ring whose underlying graded ring is graded right coherent. In this setting, the (idempotent completion of the) absolute derived category of finitely presented CDG-modules assumes the role of the bounded derived category of finitely presented modules. I will also explain how to describe the full subcategory of coacyclic CDG-modules, and how to construct the contraderived category of CDG-modules in terms of the graded-flat or graded-flat graded-cotorsion CDG-modules as an alternative to the graded-projective ones. The talk is based on two joint preprints with Jan Stovicek.

25.3 - Sergio Pavon (Univ. Padova): Torsion-simple objects
Abstract: Torsion pairs in abelian categories provide decompositions of objects, in a torsion subobject and a torsion-free quotient. Given a family F of torsion pairs, certain objects happen to be always either torsion or torsion-free with respect to each pair in F; we call them the torsion-simple objects with respect to F. Particular instances of this notion have appeared in the literature: to give one example, the semistable objects of a stability function Z are the torsion-simples with respect to a chain of torsion pairs associated to Z. In this talk we will be interested in the objects which are torsion-simple with respect to the family of all torsion pairs, in various settings (over finite-dimensional algebras, over commutative noetherian rings, in some Grothendieck hearts). This talk is partly based on arxiv:2312.04384.

18.3 - Asmae Ben Yassine (MFF UK): Approximations and Vopěnka's Principles.
Abstract: We will consider general approximation classes of modules and investigate if, and how, dualizations are possible assuming additional closure properties for these classes. While certain results can be straightforwardly dualized by employing dual arguments, other require the use of large cardinal principles such as Vopěnka's Principles. Joint work with Jan Trlifaj.

11.3 - Christoph Winges (Univ. Regensburg): Algebraic K-theory and the theorem of the heart.
Abstract: I will explain how the language of stable infinity-categories allows for a description of both connective and non-connective algebraic K-theory purely in terms of a universal property. After a discussion of Barwick’s theorem of the heart for connective algebraic K-theory, I will outline a disproof of its non-connective counterpart. This rests on showing that every spectrum can be obtained as the non-connective algebraic K-theory of some stable infinity-category. Joint work with Maxime Ramzi and Vladimir Sosnilo.

26.2 - Mikhail Gorsky (Univ. Vienna): Hall algebras and functions on categories.
Abstract: Degenerations of quantized enveloping algebras can be studied via quantum degree cones. In my work with Xin Fang, we interpreted such cones from the perspective of relative homological algebra and functor categories. In this setting, degenerations of quantized enveloping algebras and more general Hall algebras are induced by certain functions on objects in exact categories, which we call valuations, which give points in quantum degree cones. Chuang and Lazarev recently introduced another class of functions on objects in categories: rank functions on triangulated categories, generalizing, in particular, Sylvester rank functions and mass functions of Bridgeland stability conditions. In my talk, I will present some parts of my recent work with Teresa Conde, Frederik Marks, and Alexandra Zvonareva on the functorial approach to rank functions and will try to explain a connection between these frameworks. If time permits, I will explain potential applications of these methods to (quantum) cluster algebras.

29.1 - Adam-Christiaan van Roosmalen (Xi'an Jiaotong-Liverpool Univ., China): A noncommutative Kodaira vanishing theorem.
Abstract: The Kodaira vanishing theorem is a key result of complex geometry, providing the vanishing of higher cohomology groups of positive line bundles. In this talk, we discuss a possible framework to lift the Kodaira vanishing to a noncommutative geometric setting, coming from quantum flag manifolds. This talk is based on joint work with Réamonn Ó Buachalla and Jan Šťovíček.

15.1 - Alexey Ananyevskiy (LMU Munich): Combing a hedgehog over a field (part I and part II)
Abstract: A classical result in differential topology says that there are no nowhere vanishing vector fields on a 2-sphere. One may ask a similar question in algebraic geometry: does the tangent bundle to a sphere given by the equation x^2+y^2+z^2=1 over some field k have a nowhere vanishing section? Or more generally, when does the tangent bundle on an affine quadratic q=1 with q being a homogeneous degree 2 polynomial have a nowhere vanishing section? We give an essentially full answer to this question assuming that the quadric q=1 has a rational point. In particular, the 2-sphere x^2+y^2+z^2=1 over a field k has a nowhere vanishing vector field if and only if -1 is a sum of 4 squares in k. The proof uses a mixture of results from the motivic homotopy theory, Chow-Witt rings and some constructions from the theory of quadratic forms. This is a joint work with Marc Levine.

8.1. Jan Trlifaj (MFF UK): Shelah's Categoricity Conjecture for deconstructible classes of modules
Abstract: We prove the analog of Shelah's Categoricity Conjecture for all deconstructible classes of modules. More precisely, we prove the following theorem: Let R be a ring, \kappa \geq \card R an infinite cardinal, and D be a \kappa^+-deconstructible class of R-modules. Assume that D is \lambda-categorical for some cardinal \lambda \geq (2^\kappa)^+. Then D is \lambda-categorical for each cardinal \lambda \geq (2^\kappa)^+.

2023

18.12. Jan Šaroch (MFF UK): Deconstructible abstract elementary classes of modules
Abstract: We will show that if A is a deconstructible class of modules closed under direct summands, and A fits in an abstract elementary class (A,<) such that < refines direct summands, then A is closed under arbitrary direct limits. If time permits, we will also briefly discuss a version of Shelah’s Categoricity Conjecture for deconstructible classes of modules.

4.12. Chris Parker (Univ. Bielefeld): Bounded t-structures, finitistic dimensions, and singularity categories of triangulated categories
Abstract: We will talk about recent joint work on a triangulated categorical generalisation of Neeman's theorem on the existence of bounded t-structures on the derived category of perfect complexes, which solved a bold conjecture by Antieau, Gepner, and Heller. In particular, under mild conditions, we show how the existence of a bounded t-structure on the compact objects of a triangulated category T implies that the singularity category of T vanishes. To achieve this, we show that certain t-structures can be lifted from a triangulated category to its completion, as well as introduce the notion of finitistic dimension for triangulated categories. This work is joint with Rudradip Biswas, Kabeer Manali Rahul, Hongxing Chen, and Junhua Zheng.

27.11. Leonid Positselski (IM CAS): Flatness, direct limits, countability, and accessibility
Abstract: A very general category-theoretic principle, going back to an unpublished 1977 preprint of Friedrich Ulmer, tells that various category-theoretic constructions preserve the class of all \kappa-accessible categories with colimits of \lambda-indexed chains, for any regular cardinal \kappa and a smaller infinite cardinal \lambda < \kappa. Various versions of countable Govorov-Lazard theorem for flat modules, complexes, sheaves, comodules etc. can be easily obtained from this as particular cases. For example, over a countably coherent ring R, all modules of flat dimension n are direct limits of countably presented modules of flat dimension n, and all flatly coresolved modules are direct limits of countably presented flatly coresolved modules. More generally, given a sequence of classes of finitely presented R-modules S_n, n\in Z, all R-modules admitting a two-sided resolution C with the term C^n belonging to lim S_n are direct limits of countably presented modules admitting such resolutions.

20.11. Liran Shaul (MFF UK): Gorenstein acyclic complexes and finitistic dimensions
Abstract: Given a two-sided noetherian ring A with a dualizing complex, we show that the big finitistic dimension of A is finite if and only if every bounded below Gorenstein-projective acyclic cochain complex of Gorenstein-projective A-modules is contractible. If A is further assumed to be an Artin algebra, we also prove a Gorenstein variant of a theorem of Rickard, showing its finitistic dimension is finite in case its Gorenstein-injective derived category is generated by the Gorenstein-injective modules.

13.11. Souvik Dey (MFF UK): On some aspects of building modules effectively
Abstract: Given a commutative Noetherian ring, and a positive integer n, when can one build n-th syzygy of every finitely generated module from a single module by taking finite direct sums, direct summands and finitely many extensions? This is a version of the "strong generation" problem. In this talk, I will present some of the ways one can make precise sense of this and relate this to some notion of strong generation in bounded derived category, and also to some properties of annihilator ideal of Ext and Tor of modules coming from certain subcategories. We will see how these properties are inherited from similar properties of the irreducible components of the ring. Time permitting, we will also present a local-to-global principle for certain related notion of ghost index of maps. Most of the new recent results are joint with Pat Lank and Ryo Takahashi.

30.10. Sebastian Opper (MFF UK): Derived Picard groups of graded gentle algebras and integration of Hochschild classes
Abstract: The talk is based on my ongoing project concerning the derived Picard groups of graded gentle algebras, or equivalently, partially wrapped Fukaya categories of surfaces in the sense of Haiden-Katzarkov-Kontsevich. After recalling some previous results in the ungraded case, I will explain the structure of these groups and the main ingredients of its proof. As such, we discuss a projection map from the derived Picard group to the mapping class group and mapping class group actions on these categories. The last ingredient is the use of exponential maps to determine the kernel of the projection map. I will explain how they allow us to integrate certain Hochschild classes of any A-infinity-algebra over a field of characteristic 0, to elements in its derived Picard group.

23.10. Jordan Williamson (MFF UK): Purity in tensor-triangular geometry
Abstract: Tensor-triangular geometry provides a broad framework to study tensor-triangulated categories arising in nature. Just as any commutative ring has its Zariski spectrum, any tensor-triangulated category has a space called its Balmer spectrum which is the universal support theory classifying thick tensor ideals. There is also a closely related space called the homological spectrum which in all known cases is homeomorphic to the Balmer spectrum. I will explain joint work with Isaac Bird in which we build a bridge between tensor-triangular geometry and pure homological algebra, by showing that the homological spectrum can be constructed from the pure and definable structure on the triangulated category. I'll explain an application of this to functoriality in tensor-triangular geometry.

16.10. Isaac Bird (MFF UK): Coherent and definable functors for triangulated categories
Abstract: In this talk, I shall introduce coherent and definable functors for triangulated categories. The former are the purity preserving functors into finitely accessible categories with products, and generalise their namesakes as introduced by Krause. It will be shown that the restricted Yoneda embedding is the universal coherent functor. I will then introduce definable functors between triangulated categories, which will be shown to be those which preserve the pure structure. Their properties will be discussed and examples given. Time permitting, I shall give some applications to representation theory. This is based on joint work with Jordan Williamson.

9.10. Leonid Positselski (IM CAS): Countable Govorov-Lazard theorem for quasi-coherent sheaves
Abstrakt: Let X be a quasi-compact semi-separated scheme, or more generally, a stack admitting a flat affine covering by an affine scheme. I will explain how to prove that every flat quasi-coherent sheaf on X is an \aleph_1-direct limit of locally countably presented flat quasi-coherent sheaves. The argument can be spelled out in the generality of comodules over corings over noncommutative rings. Time permitting, I may also explain how to deduce the quasi-coherent cotorsion periodicity theorem for quasi-compact semi-separated schemes and some stacks. This talk is partly based on a joint work with Jan Stovicek.

2.10. Jun Maillard (MFF UK): Mackey 2-functors: a 2-categorical approach to equivariant categories
Abstrakt: In the study of representations of finite groups, the functors of restriction to a subgroup and (co)induction from a subgroup play a major role. The formalism of Mackey 2-functors abstract over these notions of restriction and induction, and let us apply techniques originating from modular representation theory to other equivariant contexts. I will present this formalism, provide examples and give results that extend to abstract Mackey 2-functors. Additionally, Mackey 2-functors can be seen as categorification of group invariants such as group cohomology and, as such, similar formulas hold for them.

26.9. Francesco Genovese (Univ. Milano Statale): Uniqueness of dg-lifts via restriction to injective objects
Abstract: Triangulated categories, and in particular derived categories, are now a classical tool in homological algebra, with many relevant applications to algebraic geometry - typically, with derived categories of sheaves on a given scheme. It is well-known that, from a theoretical point of view, triangulated categories are far from being well-behaved: there is no sensible way to define a "triangulated category of triangulated functors between triangulated categories" or a tensor product. Problems arise essentially from the failure of functoriality of mapping cones. The solution to this issue is to consider enhancements of triangulated categories: namely, viewing them as shadows of more complicated structures - for instance, differential graded (dg) categories or stable \infty-categories. If we have such enhancements, another natural question we might ask is whether triangulated functors between triangulated categories can also be upgraded to "higher" functors between such enhancements. In the geometric framework, this problem is essentially the same as the problem of existence and uniqueness of Fourier-Mukai kernels of triangulated functors between derived categories of sheaves on schemes.
In this talk, I will show a new uniqueness result for lifts of triangulated functors coming from algebraic geometry: the derived pushforward and the derived pullback (of a flat morphism between suitable schemes). The strategy is completely algebraic-categorical and involves reconstructing such lifts uniquely from their restrictions to the subcategories of injective objects.

12.6. Leonid Positselski (IM CAS): The homomorphism removal and repackaging construction
Abstract: This research grows out of an attempt to understand the Koenig-Kuelshammer-Ovsienko construction in the theory of quasi-hereditary algebras. Let k be a field and E be a k-linear exact category with a fixed family of nonzero objects F_p such that every object of E is a finitely iterated extension of some of the objects F_p. Then there is a coalgebra C over k and an exact functor from the abelian category of finite-dimensional C-comodules into E taking the irreducible (one-dimensional) C-comodules to the respective objects F_p and inducing an isomorphism of the spaces Ext^n between the irreducible C-comodules and the spaces Ext^n over F_p in E (for n > 0). So the passage from E to C-comod removes all the nontrivial homomorphisms between the objects F_p, while leaving the Ext spaces unchanged. The removed homomorphisms can then be repackaged into a semialgebra S over C so that the whole exact category E is recovered as the category of S-semimodules induced from finite-dimensional C-comodules.

22.5. Giovanna Le Gros (Univ. Padova): Generalisation of a Theorem of Bass over commutative rings

22.5. Michal Cizek (Univ. Western Ontario): Profinite graphs, automorphisms and completions
Abstract: There is an important interplay between group theory and graph theory. Using notions such as covering spaces or free actions of groups on graphs, one can describe group theoretical notions such a free and amalgamated product using graph structures. That is the foundation for Bass-Serre theory developed in the 1970s. While the covering spaces of graphs are a great tool for describing abstract groups, they are not so effective for Galois/Profinite groups, which are topological by their nature as a projective limit of finite groups. Thus, to apply the ideas from the Bass-Serre theory to profinite groups we require graphs that are topological as well. Such graphs are called profinite graphs and were extensively studied by Ribes and Zaleskii.
In the first part of this talk, we will introduce profinite graphs as projective limits of finite graphs, and introduce some basic notions on them such as their topology, connectivity and automorphisms. In the second part we will focus on an application of profinite graphs, which shows that profinite groups can be represented as a group of autohomeomorphisms of a compact space, solving a conjecture made by Sidney Morris and Karl Hoffmann. Finally, in the third part we will briefly introduce some initial ideas related to completing abstract graphs into profinite ones.
This lecture is meant for a broad audience. Its goal is to introduce the idea of adding a profinite structure on graphs and will provide some informal motivation of key notions. My research has been supported by The University of Western Ontario and Western Academy for Advanced Research.

15.5. Liran Shaul (MFF UK): Acyclic complexes and finitistic dimensions
Abstract: Over any ring, any bounded above acyclic cochain complex of projectives is null-homotopic. Similarly, any bounded below acyclic cochain complex of injectives is null-homotopic. In this talk we consider dual problems, and relate them to the finitistic dimension of the ring.

15.5. Francesco Genovese (Univ. Milano): Deforming t-structures
Abstract: A guiding principle of non-commutative algebraic geometry is that geometric objects (i.e. rings and schemes) are replaced by categories of modules/sheaves thereof. In order to keep track of the homological information, we actually take derived categories of such modules/sheaves. Under this point of view, we are now interested in understanding typical geometric concepts directly in this categorical framework. A key example is given by deformations.
In this talk, I will report on joint work with W. Lowen and M. Van den Bergh, where we attempt to define and study deformations categorically, in the framework of (enhanced) triangulated categories with a t-structure. This will also shed light on Hochschild cohomology.

24.4. Matouš Menčík (MFF UK): Inverse limits in module categories.

17.4. Amnon Yekutieli (Ben Gurion Univ.): A DG Approach to the Cotangent Complex
Abstract: Let $B/A$ be a pair of commutative rings. We propose a DG (differential graded) approach to the cotangent complex $L_{B/A}$. Using a commutative semi-free DG ring resolution of B relative to A, we construct a complex of $B$-modules $LCot_{B/A}$. This construction works more generally for a pair $B/A$ of commutative DG rings.
In the talk we will explain all these concepts. Then we will discuss the important properties of the DG $B$-module $LCot_{B/A}$. It time permits, we'll outline some of the proofs.
It is conjectured that for a pair of rings $B/A$, our $LCot_{B/A}$ coincides with the usual cotangent complex $L_{B/A}$, which is constructed by simplicial methods. We shall also relate $LCot_{B/A}$ to modern homotopical versions of the cotangent complex.

3.4.Matt Booth (Univ. Lancaster): Global Koszul duality
Abstract: Koszul duality is the name given to various duality phenomena between dg algebras and dg coalgebras involving the bar and cobar constructions. These results are usually expressed as the existence of model structures on the above categories for which the bar-cobar adjunction is a Quillen equivalence. Koszul duality can be found across many different parts of mathematics - for example, the fact that noncommutative formal moduli problems are controlled by associative algebras is the Koszul duality between dg algebras and conilpotent dg coalgebras. More familiar may be the related correspondence between formal moduli problems and dg Lie algebras, which is commutative-Lie Koszul duality.
I'll survey the above ideas and results, before turning to the global setting, where one wants to work with coalgebras that are not necessarily conilpotent - geometrically, this corresponds to using all finite-dimensional algebras as bases over which to deform, not just the Artinian local ones. I'll talk about the existence of model > structures for global Koszul duality, for which the (extended) bar-cobar adjunction is a Quillen equivalence. New here is that one has to use a new notion of weak equivalences for both algebras and coalgebras, defined in a more symmetric manner than those for usual conilpotent Koszul duality.
This is joint work with Andrey Lazarev, hopefully to appear on the ArXiv soon.

27.3. Jan Šaroch (MFF UK): Enochs' Conjecture for cotorsion pairs and more
Abstract: The Enochs Conjecture asserts that each covering class of modules (over any fixed ring) has to be closed under direct limits. We will prove the conjecture for the left hand-class of any cotorsion pair generated by (a class of) \aleph_n-presented modules for a fixed n < \omega. We also show that it is consistent with ZFC that the Enochs Conjecture holds for all classes of the form Filt(S) where S is a set of modules.

20.3. Sean Cox (VCU, Richmond): How robustly can you predict the future?
Abstract: Of all the strange consequences of the Axiom of Choice, one of my favorites is the Hardin-Taylor 2008 result that there is a "predictor" such that for every function $f$ from the reals to the reals---even nowhere continuous $f$---the predictor applied to $f \restriction (-\infty,t)$ correctly predicts $f(t)$ for *almost* every $t \in R$. They asked how robust such a predictor could be, with respect to distortions in the time (input) axis; more precisely, for which subgroups $H$ of Homeo^+(R) do there exist $H$-invariant predictors? Bajpai-Velleman proved an affirmative answer when H=Affine^+(R), and a negative answer when H is (the subgroup generated by) C^\infty(R). They asked about the intermediate region; in particular, do there exist analytic-invariant predictors? We have partially answered that question: assuming the Continuum Hypothesis (CH), the answer is "no". Regarding other subgroups of Homeo^+(R), we have affirmative answers that rely solely on topological group-theoretic properties of the subgroup. But these properties are very restrictive; e.g., all known positive examples are metabelian. So there remain many open questions. This is joint work with Elpers, Cody, and Lee.

13.3. Spyridon Afentoulidis-Almpanis (MFF UK, Prague): Dirac cohomology and the BGG category O
Abstract: Dirac operators were used in the context of representation theory by Parthasarathy in 1972, as invariant first order differential operators acting on sections of homogeneous vector bundles over symmetric spaces $G/K$ in order to obtain realizations of the discrete series representations of $G$. In a series of lectures in 1997, Vogan introduced an algebraic analogue of Parthasarthy's Dirac operator. By using this operator, he defined the so-called Dirac cohomology of $(\mathfrak{g},K)$-modules $X$ and conjectured a relation between the Dirac cohomology of $X$ and its infinitesimal character, proved by Huang and Pand\v zi\'c in 2001. Since then, Dirac cohomology has been computed for various families of modules, including highest weight modules, $A_{\mathfrak q}(\lambda)$ modules, generalized Enright-Varadarajan modules, unipotent representations, etc. In this talk, we will present some results concerning Dirac operators for modules belonging to the standard BGG category $\mathcal{O}$ of a complex semisimple Lie algebra $\mathfrak{g}$. This category consists of the finitely generated, locally $\mathfrak{n}$-finite weight modules of $\mathfrak{g}$ and seems to be the "correct" module category to study questions raised by Verma concerning composition series and embeddings of Verma modules, and Jantzen concerning his so-called translation functors.

6.3. Liran Shaul (MFF UK, Prague): Finitistic dimension, generation of injectives, and dualizing complexes
Abstract: Grothendieck showed that a commutative noetherian ring with a dualizing complex has finite Krull dimension. In this talk we explain how this generalizes to noncommutative rings via the finitistic dimension.

27.2. Chris Lambie-Hanson (IM CAS, Prague): Derived inverse limit functors and set theory
Abstract: We present some recent work applying set theoretic techniques to the study of the higher derived functors of the inverse limit functor in the context of inverse systems of abelian groups. Time permitting, we will touch on some applications of this work to the study of strong homology and condensed mathematics. This is joint work with Jeffrey Bergfalk.

20.2. Jan Šaroch (MFF UK): Enochs' conjecture for left-hand classes of cotorsion pairs

13.2. Leonid Positselski (IM CAS): Locally coherent exact categories
Abstract: This is work in progress, so the results are a bit tentative. A locally coherent exact category is a finitely accessible additive category endowed with an exact structure in which the short exact sequences are the direct limits of short exact sequences of finitely presentable objects. The category of ind-objects in any small exact category has a natural locally coherent exact category structure. Any finitely accessible additive category has a unique maximal locally coherent exact structure. In particular, the category of modules over an arbitrary ring can be endowed with the maximal locally coherent exact structure, which is intermediate between the abelian and pure exact structures on the module category. This exact structure keeps track of the short exact sequences of finitely presented modules, but disregards the short exact sequences in which the middle term and the cokernel are finitely presented while the kernel isn't. It is expected that any locally coherent exact category should be of Grothendieck type in the sense of Stovicek, leading to an application to fp-projective periodicity. An application to coderived categories is also expected.

6.2. Paolo Tomasini (SISSA, Trieste): Equivariant elliptic cohomology and mapping stacks
Abstract: The talk would be based on my joint work with my PhD supervisor Nicolò Sibilla on an approach to equivariant elliptic cohomology based on mapping stacks. Our construction produces a Hochschild homology analogue of equivariant elliptic cohomology.

24.1. Sergei Sinchuk (Munich):
Abstract: Let R be a commutative ring with unity and Ф a simple irreducible root system. Provided Ф has rank at least 2, in every group of points G(Ф,R) of a simple Chevalley—Demazure group scheme G(Ф) one can choose a normal "subgroup" generated by the so-called “elementary root unipotents” (they are generalizations of the usual transvection matrices). This group is called the elementary subgroup and is denoted E(Ф, R). The functor sending R to the quotient group G(Ф, R)/E(Ф, R) is called the unstable K1-functor of type Ф. In turn, the unstable K2-functors are defined as kernels of natural projections St(Ф,R)→E(Ф, R), where St(Ф, R) are the unstable Steinberg groups (these are certain groups given by an explicit combinatorial presentation).
It is known from the works of A. Suslin, E. Abe, H. Lindel, D. Popescu, T. Vorst and A. Stavrova that the unstable K1 groups possess the homotopy invariance property, i.e. for a regular k-algebra R one has K1(Ф, R)=K1(Ф, R[t]). This property is analogous to a particular case of Bass—Quillen conjecture, which has been originally formulated as a statement about sets Vec(n) (the pointed sets of isomorphism classes of vector bundles of constant rank n). Of course, the high-level explanation for both phenomena is that both Vec(n) and K1(Ф) are represented in the A1-homotopy category H(k) of Morel and Voevodsky. In my talk I am going to discuss to what extent the same program has been realized for the functors K2(Ф). In the end I will discuss how K2(Ф) can be presented as fundamental groups of Chevalley—Demazure group schemes G(Ф) in the category H(k).

2022

19.12. Chiara Sava (MFF UK): ∞-Dold-Kan correspondence via representation theory
Abstract: Both Happel and Ladkani proved that, for commutative rings, the quiver An is derived equivalent to the diagram generated by An where any composition of two consecutive arrows vanishes. We give a purely derivator-theoretic reformulation and proof of this result showing that it occurs uniformly across stable derivators and it is then independent of coefficients. The resulting equivalence provides a bridge between homotopy theory and representation theory; in fact we will see how our result is a derivator-theoretic version of the ∞-Dold-Kan correspondence for bounded cochain complexes.

12.12. Leonid Positselski (IM CAS): Fp-projective periodicity
Abstract: The phenomenon of periodicity, discovered by Benson and Goodearl, is related to the behavior of the modules of cocycles in acyclic complexes. It is known that all flat projective-periodic modules are projective, all fp-injective injective-periodic modules are injective, and all cotorsion-periodic modules are cotorsion. Saroch and Stovicek proved in their 2020 paper that, over a right coherent ring, all fp-projective-periodic right modules are fp-projective. I will explain how to prove that, over an arbitrary ring, all fp-projective-periodic modules are weakly fp-projective. Here the weakly fp-projective modules are the direct summands of modules filtered by the higher syzygy modules of finitely presented modules.

5.12. Manuel Eberl (University of Innsbruck): Formalising Mathematics in Isabelle/HOL
Abstract: In this talk, I give a very high-level overview about some recent work concerning the formalisation of mathematics in the interactive theorem prover Isabelle/HOL. I start with a very brief look at what Isabelle/HOL is and what formalised mathematics looks like. Then I show two particular problems that I encountered and how I solved them, namely asymptotic estimates of real-valued functions and complicated integration contours arising in Analytic Number Theory.

28.11. Ilias Kaperonis (Univ. Athens): Stabilizing PGF modules through flat modules

21.11. Leonid Positselski (IM CAS): Locality, colocality, and antilocality in cotorsion pairs over commutative rings
Abstract: Antilocality is an alternative way in which global properties of modules or complexes of modules are locally controlled in a finite affine open covering of the spectrum. For example, injectivity of modules over non-Noetherian commutative rings is not preserved by localizations, while homotopy injectivity of complexes of modules is not preserved by localizations even for Noetherian rings. The latter also applies to the contraadjustedness and cotorsion properties. All the mentioned properties of modules or complexes over commutative rings are actually antilocal. They are also colocal, if one presumes contraadjustedness. Generally, if the left class in a hereditary complete cotorsion theory for modules or complexes of modules over commutative rings is local and preserved by direct images with respect to affine open immersions, then the right class is antilocal. If the right class in a cotorsion theory for contraadjusted modules or complexes of contraadjusted modules is colocal and preserved by such direct images, then the left class is antilocal.

14.11. Francesco Genovese (MFF UK): Towards the homotopy category of derived injectives
Abstract: If A is a Grothendieck abelian category, it is a well known result that we can reconstruct the bounded below derived category D^+(A) as the bounded below homotopy category of injectives K^+(Inj(A)). On the other hand, the unbounded homotopy category of injectives K(Inj(A)) is still relevant and its features have been studied in the past years. For instance, Grothendieck duality for a (suitable) ring R can be expressed as an equivalence K(Proj(R)) = K(Inj(R)) between the unbounded homotopy categories of injective and projective R-modules. In a more general setting, we replace abelian categories and their derived categories with (enhanced) triangulated categories endowed with t-structures, sometimes called t-categories. In this setup, one can still define a suitable notion of (derived) injective/projective object and prove a reconstruction result. Instead of using classical chain complexes, though, we need the more complex notion of twisted complex. The goal of this talk is to show that the category of unbounded twisted complexes of derived injective objects is endowed with a natural t-structure and it is a suitable generalization of the homotopy category of injectives. This might have interesting future applications to dg-algebras and possibly also derived algebraic geometry.

7.11. Jan Trlifaj (MFF UK): Categoricity for transfinite extensions of modules

31.10. Michal Hrbek (IM CAS): The minimal d-tilting class over Cohen-Macaulay rings

24.10. Leonid Positselski (IM CAS): The hat equivalence and the bécarre involution II

17.10. Leonid Positselski (IM CAS): The hat equivalence and the bécarre involution
Abstract: This talk is intended as an introduction to the bécarre (\natural) construction for DG-categories. I will spell out the bécarre construction and then compute it for the DG-category of DG-modules over a DG-ring R, for which it produces the DG-category of DG-modules over another DG-ring denoted by "R with hat". The DG-ring R with hat is always acyclic, i.e., its cohomology ring is zero. Furthermore, the hat construction extends to an equivalence between the category of curved DG-rings and the category of acyclic DG-rings. Applying the bécarre construction twice to a good enough DG-category comes back to the original DG-category, while applying the hat construction twice to any CDG-ring produces a DG-ring Morita equivalent to the original one. Thus, in particular, any DG-ring R is Morita equivalent to an acyclic DG-ring "R with two hats". This version of Morita equivalence for (C)DG-rings preserves the coderived and contraderived categories, but totally destroys the conventional derived category of DG-modules.

10.10. Simion Breaz (Babes-Bolyai Univ., Cluj-Napoca): Baer-Kaplansky Theorem and heaps of modules

29.9. Roger Wiegand (Univ. Nebraska): Homological properties of quasi-fiber-product rings

29.9. Sylvia Wiegand (Univ. Nebraska): Vanishing of Ext for quasi-fiber product rings

15.8. Po Hu (Wayne State Univ.): The Z/p-Equivariant Steenrod Algebra for odd primes
Abstract: I will discuss recent joint work by Po Hu, Igor Kriz, Petr Somberg, and Foling Zou https://arxiv.org/abs/2205.13427 calculating the Z/p-equivariant Steenrod algebra for odd primes. I will discuss the result, some specific new tools necessary for this calculation, as well as some potential applications.

15.8. Igor Kříž (Univ. Michigan): Equivariant Topology and the Steenrod Algebra
Abstract: In this talk, we will introduce some concepts of equivariant algebraic topology. We will also discuss the concept of cohomological operations and the Steenrod algebra. We will then present a classical calculation of the Z/2-equivariant Steenrod algebra by Hu and Kriz, and its significance in equivariant topology, including Hill, Hopkins, and Ravenel's solution of the Kervaire invariant 1 problem.

24.5. Septimiu Crivei (B.B.Univ. Cluj): Maximal Exact Structures on Additive Categories
Abstract: Quillen exact categories have recently reappeared into the mainstream due to some new applications to algebraic K-theory, model structures, approximation theory or functional analysis. They provide a suitable setting for developing homological algebra beyond abelian categories, as is often the case in the above settings. Every additive category has an obvious smallest exact structure given by the split exact sequences. It is natural to wonder whether there exists, and then which is, the greatest exact structure on an arbitrary additive category. We review known results for preabelian, weakly idempotent complete and additive categories, and we present some steps towards its description.

23.5. Jakub Kopřiva (MFF UK): Semiorthogonal decompositions for gentle algebras
Abstract: The bounded derived category of a gentle algebra can be studied using curves on some marked surface. In this talk, I will give a characterization of semiorthogonal decompositions of the bounded derived category as certain ways how to cut the associated marked surface. This is a joint work with Jan Šťovíček.

16.5. Liran Shaul (MFF UK): Finitisic dimensions over commutative DG-rings
Abstract: Over a ring A, the big projective finitistic dimension FPD(A) is defined to be the supremum of projective dimensions of all A-modules of finite projective dimension. When A is commutative and noetherian, classical results of Bass and Raynaud-Gruson showed it is always equal to the Krull dimension of A. In this talk I will discuss the corresponding problem for commutative DG-algebras and its solution. This is based on a joint work with Isaac Bird, Prashanth Sridhar and Jordan Williamson.

9.5. Zahra Nazemian (Univ. Graz): Bounded factorization property for some classes of noetherian domains
Abstract: Besides several techniques to find examples of noetherian domains with bounded factorization (BF) property, we will show that noetherian domains possessing a particular finite partition function from finitely generated modules to a set of ordinals are BF. This implies that noetherian rings with Auslander dualizing complex are BF. Examples of these rings include noetherian Hopf algebras (including the group algebra kG where k is a field and G a polycyclic-by-finite group) and the Weyl algebras A_n(k) where k is a field of characteristic zero. (Based on joint work with J. Bell, K. Brown, and D. Smertnig.)

2.5. Jan Šťovíček (MFF UK): t-Structures cogenerated by pure-injective objects

25.4. Lorenzo Martini (Univ. Verona): Cotilting duality for artinian rings
Abstract: A classical result due to Morita and Azumaya establishes that any duality between the finitely generated modules over two arbitrary rings is representable by a unique bimodule which is a finitely generated injective cogenerator on both sides and, moreover, the two rings are necessarily artinian. We generalise this well-known result to the "cotilting duality", i.e. to the duality induced by a cotilting bimodule regarded in the derived categories of the given rings.

11.4. Leonid Positselski (IM CAS): Nonhomogeneous quadratic duality II

31.3. Yilmaz Durgun (Cukurova Univ. Adana): The opposite of projectivity by proper classes
Abstract: Proper classes (or exact structures) offer rich research topics due to their important roles in category theory. Motivated by the researches on opposite of projective modules, we investigate projectively generated proper classes. As an opposite to projectivity, a module M is said to be π-indigent if the projectively generated proper class by M is the smallest possible, namely, consisting of exactly the split short exact sequences. While when every module over a ring R is projective or when every module is π-indigent, R is semisimple artinian, rings over which every right module is either projective or π-indigent are not necessarily semisimple artinian. We show that every (finitely generated, finitely presented, cyclic, simple) right R-module is either projective or π-indigent if and only if R is Artinian serial and J2(R)=0 with a unique singular simple module (up to isomorphism). We initiate a deep study of the class of all projectively generated proper classes and denote it by π(R) for the ring R. We analyze the class π(R) in details. Among other results, we show that π(R) is linearly ordered if and only if |π(R)|=2, i.e., every non-projective module is π-indigent. Moreover, we show that, for each singular simple right R-module A, the projectively generated proper class by A is a maximal element of π(R). Under suitable conditions, the poset (π(R),⊆) turns out to be a bounded complete lattice, and it is boolean if R is an Artinian serial ring and J2(R)=0.

28.3. Aleksei Tsybyshev: Advances in Voevodsky's explicit approach to the stable homotopy category SH(k) of k-smooth varieties
Abstract: V. Voevodsky, together with F. Morel, defined the stable homotopy category SH(k) of k-smooth varieties and showed its many good properties. However, that construction is implicit and computations within it are hard. Voevodsky later proposed another approach to this category, more akin to the construction of the category DM of motives via Cor-sets of correspondences. This idea was developed in the works of G. Garkusha, I. Panin and others. This talk aims to introduce the main concepts of the area in an accessible and coherent way, and formulate some of the main results and their generalisations, for example, giving new ways to (locally) compute motivic homotopy sheaves π_{m,n} (X).

21.3. Alexandra Zvonareva (Uni. Stuttgart): Functorial approach to rank functions

14.3. Wassilij Gnedin (Uni. Bochum): Silting theory under change of rings

7.3. Leonid Positselski (IM CAS): Nonhomogeneous quadratic duality
Abstract: Nonhomogeneous quadratic duality is a fully faithful contravariant functor from the category of nonhomogeneous quadratic algebras, which means filtered rings with increasing filtrations whose associated graded rings are quadratic, to the category of quadratic CDG-algebras. The functor becomes an anti-equivalence when restricted to the categories of nonhomogeneous Koszul algebras and Koszul CDG-algebras. I will explain the main concepts involved and present the basic elements of the construction of the duality. Time permitting, I may say a few words about the relative case over a base ring instead of a field.

28.2. Michal Hrbek (MI CAS): Topological endomorphism rings of tilting complexes II

21.2. Michal Hrbek (MI CAS): Topological endomorphism rings of tilting complexes

14.2. Pavel Příhoda (MFF UK): A version of the Govorov-Lazard theorem for flat modules generated by a given projective

10.1. Georgios Dalezios (Univ. Athens): Linear Reedy categories and abelian model structures
Abstract: Reedy categories form a generalization of the category of finite ordinals, with morphisms the weakly monotone functions, and are of fundamental importance in topology. In this talk, we discuss linear versions of Reedy categories and relate them to quivers with relations and finite-dimensional algebras. We also present a result on lifting complete cotorsion pairs and abelian model structures from certain abelian categories to functors indexed by linear Reedy categories. The talk is based on discussions with Jan Stovicek.

3.1. Leonid Positselski (IM CAS): A covering class of modules not closed under pure quotients
Abstract: I will present an example of a Bass flat brick module F over an associative algebra R (over a field k) with a projective pure submodule P in F such that the quotient module F/P does not belong to Add(F). Thus Add(F) is a covering class of R-modules, which is closed under direct limits, but not under pure epimorphic images. The k-algebra R is constructed in terms of a certain infinite quiver with relations, and can be thought of as universal in some sense.

2021

6.12. Jan Trlifaj (MFF UK): Weak diamond and weak projectivity

29.11. Prashanth Sridhar (MFF UK): Finding Maximal Cohen-Macaulay modules: Representation stability and outer automorphism groups
Abstract: In this talk, we consider a problem that lies in the confluence of two topics. On one hand, we have maximal Cohen-Macaulay (MCM) modules - these are classical objects that have been studied extensively from algebraic and geometric viewpoints. There is a rich theory of MCM modules over Cohen-Macaulay (CM) rings and many beautiful connections to the singularities of the ring have been discovered. However, in the absence of the CM property in the ring, not as much is known - even the object's existence is largely unclear. On the other hand, we have a mixed characteristic phenomenon. In 1980, Paul Roberts showed that the integral closure of a regular local ring in an Abelian extension of its quotient field is CM, provided the characteristic of the residue field does not divide the degree of the extension. This fails in the "modular case" in mixed characteristic. We will look at some past results in the literature before considering the question of existence of MCMs in the modular case of Roberts's theorem.

22.11. Luca Pol (Univ. Regensburg): Representation stability and outer automorphism groups
Abstract: In this talk, I will present a framework for studying families of representations of the outer automorphism groups indexed on a collection of finite groups U. One can encode this large amount of data into a convenient abelian category AU which generalizes the category of VI-modules appearing in the representation theory of the finite general linear groups. Inspired by the work of Church-Ellenberg-Farb, I will discuss for which choices of U the abelian category is locally noetherian and deduce analogues of central stability and representation stability results in this setting.

15.11. Asmae Ben Yassine (MFF UK): Flat relative Mittag-Leffler modules and approximations

8.11. Sebastian Opper (MFF UK): Brauer graph algebras and their derived equivalence classification

1.11. Jan Šťovíček (MFF UK): On the topological coperfectness problem

25.10. Jan Trlifaj (MFF UK): Direct limit closures in module categories

11.+18.10. Leonid Positselski (IM CAS, Prague): The Govorov-Lazard problem for contramodules over topological rings
Abstract: The classical Govorov-Lazard theorem tells that any flat module over a ring is a direct limit of finitely generated free modules. The aim of this talk is to report on recent progress concerning the same question for contramodules over topological rings. A counterexample shows that the class of flat contramodules can be wider than the class of all direct limits of projective contramodules, at least if one considers topological rings having no countable base of neighborhoods of zero. On the other hand, under certain restrictive assumptions on the topological ring one can prove that all flat contramodules are direct limits of finitely generated projective or free ones. I will also discuss the related concepts of 1-strictly flat and infinity-strictly flat contramodules as well as contratensor purity.

24.5. Jordan Williamson (MFF UK): Local Gorenstein duality in chromatic group cohomology
Abstract: Many algebraic definitions and constructions can be made in a derived or homotopy invariant setting and as such make sense for ring spectra. Dwyer-Greenlees-Iyengar (followed by Barthel-Heard-Valenzuela) showed that one can make sense of local Gorenstein duality for ring spectra. In this talk, I will show that cochain spectra C*(BG;R) satisfy local Gorenstein duality surprisingly often, and explain some of the implications of this. When R=k is a field this recovers duality properties in modular representation theory conjectured by Benson and later proved by Benson-Greenlees. However, the result also applies to more exotic coefficients R such as Lubin-Tate theories, K-theory spectra or topological modular forms, showing that chromatic analogues of Benson’s conjecture also hold. This is joint work with Luca Pol.

17.5. Liran Shaul (MFF UK): The structure of derived categories of commutative DG-rings
Abstract: The notion of stratification of a triangulated category with an action by a graded ring was introduced by Benson, Iyengar and Krause. This notion allows one to classify the localizing subcategories of such a triangulated category, giving a formal framework to a foundational result of Neeman who proved such a classification for the derived category of a commutative noetherian ring. In this talk we explain a necessary and sufficient condition which allows to lift such a stratification between certain tensor triangulated categories. As an application, we are able to completely classify the localizing and colocalizing subcategories of the derived categories of a wide variety of commutative DG-rings.
This talk is based on a joint work with Jordan Williamson.

30.4. Pavel Příhoda (MFF UK): Universal localizations of some serial rings

12.4. Sergio Pavon (Univ. Padova, MU AVCR): Derived equivalences via iterated HRS-tilting, for commutative noetherian rings
Abstract: The title of this talk refers to that of a paper by Chen, Han and Zhou (Derived equivalences via HRS-tilting, Adv. Math. 354, 2019), which is used as a starting point. In it, the authors provide a criterion for the HRS-tilting at a torsion pair in an abelian category A to give a t-structure with heart (bounded) derived equivalent to A. We refine the criterion for hereditary torsion pairs in Grothedieck categories, and then proceed to apply it several times inside the derived category D(R) of a commutative noetherian ring R. We deduce:
1) that all hereditary torsion pairs in Mod(R) induce derived equivalence, via HRS-tilting;
2) that all intermediate compactly generated t-structures in D(R) which restrict to the bounded derived category of finitely presented R-modules have heart derived equivalent to Mod(R), via iterated HRS-tilting.
This talk is based on joint work with J.Vitória, arXiv:2009.08763.

29.3. Jan Šaroch (MFF UK): Enochs conjecture for small precovering classes

15.3. Sean Cox (Virginia Commonwealth Univ., Richmod, USA): Vopěnka's Principle and completeness of cotorsion pairs

8.2. Michal Hrbek (IM CAS, Prague): Gluing of t-structures over stalks of affine schemes
Abstract: We show that compactly generated t-structures in the derived category of a commutative ring R correspond bijectively to certain families of compactly generated t-structures over the localizations of R at maximal ideals. These compatible families are given by a natural gluing condition for the associated sequence of Thomason subsets of the Zariski spectrum. As one application, we show that the compact generation of a homotopically smashing t-structure can be checked locally at maximal ideals. Together with a result of Balmer and Favi, this yields that the Telescope Conjecture over a concentrated scheme is a stalk-local property. Furthermore, we show that derived colocalization functors induce a bijection between cosilting objects of cofinite type over R and compatible families of cosilting objects of cofinite type over stalks of R, generalizing the result of Trlifaj and Şahinkaya. This is a report on recent joint work with JiangshengbHu and Rongmin Zhu.

1.2. Leonid Positselski (IM CAS, Prague): Exact category structures and tensor products of topological vector spaces with linear topology
Abstract: Abelian categories are rare in functional analysis or topological algebra, and the classical approach to developing homological algebra in topological settings has been to construct and use exact category structures. The quasi-abelian categories form a class of additive categories closest to the abelian ones; they have very natural exact category structures. The categories of all topological vector spaces or Hausdorff topological vector spaces are quasi-abelian, but the category of complete topological vector spaces is not, because the quotient space of a complete topological vector space by a closed subspace need not be complete. I will explain that the category of complete Hausdorff topological vector spaces is right, but not left quasi-abelian, contrary to a claim on the first page of a 2008 paper of Beilinson. Furthermore, Beilinson defined three important tensor product operations on topological vector spaces with linear topology and claimed that they are exact functors in the (nonexistent) quasi-abelian exact category structure. I will explain that at least two of the three tensor products are not exact in the maximal exact structure on topological vector spaces.

2020

30.11. Ilya Smirnov (MFF UK): Some improvements of Lech's inequality
Abstract: In 1960, Lech found an inequality connecting two basic invariants of an m-primary ideal of a local ring R: colength and multiplicity. Lech observed that his inequality is never sharp in dimension at least two. In my talk, I will explain why Lech's inequality is natural and present several improvements.

9.11. Jan Šťovíček (MFF UK): Mutation of inifinitely generated cosilting modules

19.10. Jiangsheng Hu (Jiangsu Univ. Tech.): From recollements of abelian categories to recollements of triangulated categories
zoom-talk (mp4), slides (pdf).

12.10. Leonid Positselski (IM CAS, Prague): A description of the second class in the cotilting cotorsion pair in terms of cofiltrations
slides, paper on arXive
Abstract : Saroch and Trlifaj in their recent paper described the right class in the cotorsion pair induced by any 1-cotilting module in terms of 2-step filtrations by injective modules and products of copies of the cotilting module. This result was based on the classical dual Bongartz lemma. In this talk, I will formulate the n-Bongartz lemma for an integer n and show how to use the dual n-Bongartz lemma in order to describe the right class in the cotorsion pair induced by any n-cotilting module in terms of (n+1)-step filtrations by products of copies of the associated i-cotilting modules, where i ranges from 0 to n. The dual description of the left class in any n-tilting cotorsion pair also holds.

5.10. Liran Shaul (MFF UK): Koszul complexes over Cohen-Macaulay rings
Abstract : It is well known that if A is a Cohen-Macaulay ring and $a_1,\dots,a_n$ is an $A$-regular sequence, then the quotient ring $A/(a_1,\dots,a_n)$ is also a Cohen-Macaulay ring. In this talk we explain that by deriving the quotient operation, if A is a Cohen-Macaulay ring and $a_1,\dots,a_n$ is any sequence of elements in $A$, the derived quotient of $A$ with respect to $(a_1,\dots,a_n)$ is Cohen-Macaulay.

8.6. Jordan Williamson (Univ. Sheffield): Algebraic models for change of groups functors
Abstract: Equivariant cohomology theories are powerful invariants of spaces with the action of a group. A conjecture of Greenlees states that when one restricts to the equivariant cohomology theories taking values in rational vector spaces, there is an abelian category equivalent to it. This conjecture has been proven in many cases; for example for finite groups, for tori of any rank, or for equivariant cohomology theories on spaces with a free action. The inclusion of a subgroup H into a compact Lie group G induces an adjoint triple of induction, restriction and coinduction functors between the categories of G-equivariant cohomology theories and H-equivariant cohomology theories, analogous to the functors in representation theory. In this talk, I will explain how to connect the induction, restriction and coinduction functors in topology with functors in algebra. I will attempt to focus on the more algebraic aspects of this story, in particular, the Gorenstein condition in derived commutative algebra context.

8.6. Leonid Positselski (IM CAS, Prague): A construction of complete cotorsion pairs in the relative context
Abstract: Let R -> A be a ring homomorphism, and let (F,C) be a hereditary complete cotorsion pair in R-Mod. Let (F_A,C_A) be the cotorsion pair in A-Mod for which F_A is the class of all A-modules whose underlying R-modules belong to F. Assuming that countable products of modules from F have finite F-resolution dimension bounded by a natural number k and the class F is preserved by the functor Hom_R(A,-), we show that C_A is the class of all direct summands of A-modules cofiltered by A-modules coinduced from modules from C, with the cofiltrations indexed by the ordinal omega+k.

1.6. Issac Bird (Univ. Manchester): Definable classes arising from maximal Cohen-Macaulay modules
Abstract: Over a Cohen-Macaulay ring the most well known extension of the maximal Cohen-Macaulay modules is the class of balanced big Cohen-Macaulay modules, however, this class does not have particularly nice closure properties, such as not always being closed under summands. I will describe two definable classes, which have particularly nice closure properties, extending both the maximal and balanced big Cohen-Macaulay modules, describe the relationship between the two and discuss some of their properties. I will then give a particular application over hypersurface rings by discussing the relationship between Ziegler spectrum of the Gorenstein flat modules and Knoerrer periodicity.

11.5. Pavel Růžička (MFF UK): Realization of Riesz refinement monoids by von Neumann regular rings
Abstract: The commutative monoid V(R), assigned to a unital associative ring R, consists of all isomorphism classes of finitely generated projective right R-modules, with the operation induced from direct sums. If R is a von Neumann regular ring or a C∗-algebra with real rank zero, then the monoid V(R) satisfies the Riesz refinement property. We will discuss the realization problem, whether every countable monoid with the Riesz refinement property is isomorphic to the monoid V(R) of a von Neumann regular ring.

4.5. Sebastian Opper (Univ. Paderborn): A surface model for cycles of projective lines and applications
Abstract: Polishchuk showed that spherical objects in the derived category of any cycle of projective lines yield solutions of the associative Yang-Baxter equation which raises the question whether one can classify spherical objects in this case. He further posed the question whether the group of derived auto-equivalences of a cycle acts transitively on isomorphism classes of spherical objects. Partial solutions to both problems were given in works of Burban-Kreussler and Lekili-Polishchuk. A theorem of Burban-Drozd establishes a connection between the derived category of any cycle of projective lines with the derived category of a certain gentle algebra. The derived categories of such algebras can be modelled by a (toplogical) surface which allows to translate algebraic information in the derived category such as objects into geometric information on the surface such as curves. I will explain how the result of Burban-Drozd can be used to find a similar model for the derived category of a cycle. In the final part of the talk, I will show how the surface model can be used to classify spherical objects and establish transitivity for any cycle of projective lines. We will discuss further applications to their groups of derived auto-equivalences and faithfulness of certain groups actions as defined by Sibilla.

23.3. Leonid Positselski (MI, CAS): Derived adically complete modules and complexes
Abstract: Let I be a finitely generated ideal in a commutative ring R. Several definitions of derived I-adically complete complexes of R-modules exist in the literature. I will explain that there are, in fact, three reasonable triangulated categories of derived I-adically complete complexes arising from two abelian categories of derived I-adically complete R-modules. There are also two triangulated categories of derived I-torsion complexes related to one abelian category of I-torsion R-modules. When the ideal I is weakly proregular (in particular, when the ring R is Noetherian), there is only one category in each case.

11.3. Tsutomu Nakamura (Univ. Verona): Cosupport and related topics

9.3. Liran Shaul (MFF UK): Open loci results for commutative DG-rings
Abstract: The aim of this lecture is to describe the generic local structure of an eventually coconnective derived scheme. To do this, we introduce the regular, Gorenstein and Cohen-Macaulay loci of a commutative differential graded ring. We study these loci, and explain that while the regular and Gorenstein loci are often empty, under mild assumptions the Cohen-Macaulay locus of a commutative DG-ring contains a dense open set.

2.3. Jan Šaroch (MFF UK): Enochs conjecture for Add(M) 

24.2. Edoardo Lanari (MU AVCR): Infinite powers of approximating ideals
Abstract: The goal of this talk is to describe an equivalence between the (∞,2)-category of cartesian factorization systems on ∞-categories and that of pointed cartesian fibrations of ∞-categories. This generalizes a similar result known for ordinary categories and sheds some light on the interplay between these two seemingly distant concepts.

18.2. Xianhui Fu (Northeast Normal Univ. Changchun): Infinite powers of approximating ideals
Abstract: In this talk, we present and prove an ideal version of Eklof's Lemma. After introducing the notion of the \alpha-th inductive power of a special preenveloping ideal for an ordinal \alpha, we show that the \alpha-th inductive power of a special preenveloping ideal is still special preenveloping for any ordinal \alpha. As applications, we prove that if $R$ is a right coherent ring and the class of pure projective right $R$-modules is closed under extensions, then every FP-projective module is pure projective; and show that in the derived category of modules over a ring $R$, the \aleph_0-th inductive power of the ghost ideal is zero. This talk is based on a joint work with Ivo Herzog, Sergio Estrada, and Sinem Odabasi.

13.1. Leonid Positselski (IM CAS): PRECOVERS AND COVERS OF DIRECT LIMITS OF MODULES AND CONTRAMODULES
Abstract: There are two main results to be explained in this talk: 1. a simple elementary proof of the Enochs conjecture for the left class of an n-tilting cotorsion pair in a Grothendieck category, and 2. a direct limit of projective contramodules is projective if it has a projective cover. Both results are obtained from an argument about precovers and covers of direct limits, based on considerations of local splitness. This talk is based on a joint work with Silvana Bazzoni and Jan Stovicek.

6.1. Jan Stovicek (MFF UK): T-STRUCTURES AND LOCALIZATIONS OF CATEGORIES

2019

16.12. Jiangsheng Hu (Jiangsu University of Technology, Changzhou, China): SPECIAL PRECOVERING CLASSES IN COMMA CATEGORIES
Abstract：Let T be a right exact functor from an abelian category B into another abelian category A. Then there exists a functor p from the product category A x B to the comma category (T ↓ A). In this talk, we study the property of the extension closure of some classes of objects in the comma category (T ↓ A), the exactness of the functor p and the detail description of orthogonal classes of a given class induced by p. Moreover, we characterize when special precovering classes in abelian categories A and B can induce special precovering classes in (T ↓ A). As an application, we prove that under suitable cases, the class of Gorenstein projective left Λ-modules over a triangular matrix ring Λ is special precovering if and only if both the classes of Gorenstein projective left R-modules and left S-modules are special precovering. Consequently, we produce a large variety of examples of rings such that the class of Gorenstein projective modules is special precovering over them. The talk is based on a recent joint work with Haiyan Zhu.

9.12. Jan Stovicek (MFF UK): PERFECT DECOMPOSITIONS OF MODULES AND COPERFECTNESS OF TOPOLOGICAL RINGS

2.12. Jan Saroch (MFF UK): APPROXIMATION PROPERTIES OF GORENSTEIN PROJECTIVE MODULES OVER A GENERAL RING

25.11. Martin Mach (MFF UK): ON THE LINES ON DEGREE 4 AND OTHER DEL PEZZO SURFACES
Abstrakt: Del Pezzo surfaces are smooth projective algebraic surfaces with an ample anti-canonical divisor. Over an algebraically closed field they can all be obtained by blowing up the projective plane or as a product of two projective lines. Most famously, blowing up the plane in 6 points gives us the cubic surface. It has been known since 1849 due to Cayley, that this surface contains 27 straight lines (most succintly descibed as -1-curves).
We look at the case of the Segre surface, which is a smooth intersection of two quadrics in projective 4-space. It is known to contain 16 straight lines. We adapt Cayley's method to show an existence of at least one line on the surface. Then we turn to divisor theory to enumerate the lines for many of del Pezzo surfaces simultaneously.

18.11. Jakub Kopřiva (MFF UK): STABILITY CONDITIONS AND RING EPIMORPHISMS II

11.11. Leonid Positselski (MU AVCR): RINGS OF QUOTIENTS W. R. T. GABRIEL FILTERS: FLATNESS VS. EPIMORPHISM PROPERTY II

4.11. Claire Voisin (College de France): RATIONALITY PROBLEMS AND DECOMPOSITION OF THE DIAGONAL
The (stable) rationality problem consists in deciding whether a smooth projective variety is (stably) rational or not. I will describe an obstruction to (stable) rationality for a smooth projective variety defined over an algebraically closed field which originates in the work of Bloch and Srinivas. The specialization method that I introduced a few years ago led to many new (stable) irrationality results and the discovery of interesting new stable birational invariants.

21.10. Leonid Positselski (MU AVCR): RINGS OF QUOTIENTS W. R. T. GABRIEL FILTERS: FLATNESS VS. EPIMORPHISM PROPERTY

14.10. Amnon Yekutieli (Ben Gurion Univ.): FLATNESS AND COMPLETION REVISITED
Abstract: In this talk I consider an old and exhaustively studied situation: A is a commutative ring, and \a is an ideal in it. ("\a" stands for gothic "a".) We are interested in the \a-adic completion operation for A-modules, and in flatness of A-modules.
The departure from the classical and familiar situation is this: the A-modules we care about are not finitely generated. The following was considered an open problem by commutative algebraists: if A is a noetherian ring and M is a flat A-module, is the \a-adic completion of M also flat? Partial positive answers were published in the literature over the years. In 2016 I found a proof of the general case. But then, a series of emails led me to prior proofs, that are embedded in pretty recent texts, and were unknown to the commutative algebra community.
Nonetheless, my methods gave more detailed variants of the general result mentioned above, that are actually new. One of them concerns the case of a ring A that is not noetherian, but where the ideal \a is weakly proregular. The latter is a condition discovered by Grothendieck a long time ago, but became prominent only very recently (in the context of derived completion).
In the talk I will give the background, mention the new and not-so-new results (with some proofs), and give a few concrete examples.

7.10. Alexander Slavik (MFF UK) ON FLAT GENERATORS AND MATLIS DUALITY FOR QUASICOHERENT SHEAVES
Abstract: We show that for a quasicompact quasiseparated scheme X, the following assertions are equivalent: (1) the category QCoh(X) of all quasicoherent sheaves on X has a flat generator; (2) for every injective object E of QCoh(X), the internal hom functor into E is exact; (3) the scheme X is semiseparated. Joint work with Jan Šťovíček.

10.9. Miroslav Ploščica (TU Košice): TOPOLOGICAL REPRESENTATIONS OF CONGRUENCE LATTICES

27.5. Jakub Kopřiva (MFF UK): STABILITY CONDITIONS AND RING EPIMORPHISMS

13.5. Oleh Romaniv (IFNU Lviv): J-NOETHERIAN BEZOUT DOMAIN WHICH ARE NOT OF STABLE RANGE 1. A BEZOUT RING OF STABLE RANGE 2 WHICH HAS SQUARE STABLE RANGE 1
slides(pdf)
Abstract: In this talk we explain how to extend the theory of Cohen-Macaulay rings and Cohen-Macaulay modules to the setting of commutative DG-rings. We will explain how by studying local cohomology in the DG-setting, one obtains certain amplitude inequalities about certain DG-modules of finite injective dimension. When these inequalities are equalities, we arrive to the notion of a Cohen-Macaulay DG-ring. We show that these arise naturally in many situations, and explain their basic theory. The talk is based on arxiv:1902.06771.

7.5. Tsutomu Nakamura (Univ. Verona): PURE DERIVED CATEGORIES AND BIG COHEN-MACAULAY MODULES

6.5. Bohdan Zabavsky (IFNU Lviv): CONDITIONS FOR STABLE RANGE OF ELEMENTARY DIVISOR RINGS
slides 1 (pdf), slides 2 (pdf)

15.4. Jan Šaroch (MFF UK): TESTING FOR PROJECTIVITY OF MODULES OF FINITE PROJECTIVE DIMENSION

8.4. Leonid Positselski (IM CAS): SPLIT CONTRAMODULE CATEGORIES ARE SEMISIMPLE

1.4. Michal Hrbek (MU AVCR): ON T-STRUCTURES ARISING FROM A CHAIN OF RING EPIMORPHISMS

18.3. Rongmin Zhu (Nanjing Univ.): RECOLLEMENTS ASSOCIATED TO COTORSION PAIRS OVER UPPER TRIANGULAR MATRIX RINGS

11.3. Liran Shaul (MFF UK): THE COHEN-MACAULAY PROPERTY IN DERIVED ALGEBRA
Abstract: In this talk we explain how to extend the theory of Cohen-Macaulay rings and Cohen-Macaulay modules to the setting of commutative DG-rings. We will explain how by studying local cohomology in the DG-setting, one obtains certain amplitude inequalities about certain DG-modules of finite injective dimension. When these inequalities are equalities, we arrive to the notion of a Cohen-Macaulay DG-ring. We show that these arise naturally in many situations, and explain their basic theory. The talk is based on arxiv:1902.06771.

4.3. Leonid Positselski (IM CAS): COUNTABLY GENERATED ENDO-SIGMA-COPERFECT MODULES
Abstract: A question of Angeleri Hugel and Saorin about perfect decompositions of endo-Sigma-coperfect modules can be formulated as follows: if a module M is Sigma-coperfect over its endomorphism ring, does it follow that every local direct summand in M is a direct summand? In this talk I will prove that if M is a countably generated endo-Sigma-coperfect module, then every countably indexed local direct summand in M is a direct summand. The argument using Bass flat contramodules over topological rings with a countable base of neighborhoods of zero belongs to Jan Stovicek and the speaker.

25.2. Jan Saroch (MFF UK): ON A RECURSIVE NOTION OF RELATIVE STATIONARITY FOR MODULES

18.2. Alexander Slavik (MFF UK): FLAT GENERATORS OF QUASICOHERENT SHEAVES

11.2. Roger Wiegand (University of Nebraska): TORSION IN TENSOR PRODUCTS

11.2. Sylvia Wiegand (University of Nebraska): PRIME IDEALS IN RINGS OF POWER SERIES AND POLYNOMIALS
Abstract

7.1. Leonid Positselski (IM CAS): COMMUTATIVE TOPOLOGICALLY PERFECT RINGS

2018

17.12. Leonid Positselski (IM CAS): TOPOLOGICALLY PERFECT RINGS

10.12. Jan Trlifaj (MFF UK): FAITH'S PROBLEM FOR SEMIARTINIAN VON NEUMANN REGULAR RINGS

3.12. Leonid Positselski (IM CAS): A TOPOLOGICAL CHARACTERIZATION OF MODULES WITH PERFECT DECOMPOSITIONS
Abstract: A module (over some associative ring) is said to have a perfect decomposition if it decomposes as a direct sum of a family of modules satisfying a kind of local T-nilpotency condition for all noninvertible morphisms between modules in the family. It turns out that modules with perfect decomposition can be characterized in terms of their topological rings of endomorphisms: a module has perfect decomposition if and only if its topological ring of endomorphisms has strongly closed topologically T-nilpotent (topological) Jacobson radical, and the topological quotient ring is topologically semisimple. One can call such topological rings "topologically perfect". For example, a commutative topological ring is topologically perfect if and only if all its discrete quotient rings are perfect.

26.11. Leonid Positselski (IM CAS): TOPOLOGICALLY SEMISIMPLE TOPOLOGICAL RINGS
Abstract: A Grothendieck abelian category is said to be semisimple if every its object is a (direct) sum of simple objects. The property of an associative ring to have a semisimple module category is left-right symmetric (such rings are called classically or Artinian semisimple). In this talk I will prove a similar theorem for topological rings: the abelian category of left contramodules over a topological ring R is Grothendieck and semisimple if and only if the abelian category of discrete right R-modules is semisimple. Time permitting, I may also say a few words about a conjectural notion of a topologically left perfect ring.

19.11. Liran Shaul (MFF UK): INJECTIVE MODULES OVER DERIVED RINGS
Abstract: The notion of an injective module is fundamental in homological algebra over rings. In this talk, we explain how to generalize this notion to derived rings. The Bass-Papp theorem states that a ring is left noetherian if and only if direct sums of left injective modules are injective. We will explain a version of this result in higher algebra, leading us to the notion of a left noetherian derived ring. In the final part of the talk, we will specialize to commutative noetherian derived rings, show that the Matlis structure theory of injective modules holds in this setting, and deduce a generalization of Grothendieck’s local duality theorem.

12.11. Alexander Slávik (MFF UK): PURITY IN CATEGORIES OF SHEAVES
There are (at least) two types of purity considered for the category of sheaves over a scheme (either quasicoherent or not): the geometric one, defined using the tensor product, and the categorical one, defined via finitely presented objects. We investigate the properties of and the relations between these two. Most importantly, for a quasicompact and quasiseparated scheme X, the two purities in QCoh(X) coincide if and only if X is affine. Time permitting, a number of (counter)examples will be presented. Joint work with Mike Prest.

5.11. Leonid Positselski (IM CAS): FLAT COMMUTATIVE RING EPIMORPHISMS OF ALMOST KRULL DIMENSION ZERO
Abstract: I will explain how to prove that a flat epimorphism of commutative rings has projective dimension at most one provided that, in the related Gabriel filter of ideals, the quotient ring by any ideal in the filter is semilocal of Krull dimension zero. The argument is based on the notion of an I-contramodule R-module for an ideal I in a commutative ring R.

29.10. Georgios Dalezios (Univ. Murcia): A SURVEY OF GORENSTEIN HOMOLOGICAL ALGEBRA

22.10. Liran Shaul (MFF UK): WHAT IS DERIVED COMMUTATIVE ALGEBRA?
Abstract: Derived commutative algebra is the result of mixing ideas from commutative algebra with homotopy theory. The purpose of this talk is to explain some of the basic ideas of derived commutative algebra. I will give various examples demonstrating how classical commutative algebra misses some key information about various homological constructions, and show how by using derived commutative rings one may retain this information and prove stronger results.

1.10., 8.10., and 15.10. Leonid Positselski (IM CAS): HOW TO PROVE THAT A FLAT RING EPIMORPHISM HAS PROJECTIVE DIMENSION ONE?
Abstract: The aim of this series of talks is to explain the details of a technique for proving that, in some left flat ring epimorphisms, the projective dimension of the target ring as a left module over the source does not exceed one. Two assertions are known to be provable with two versions of the technique. One of them is that a left flat epimorphism of associative rings has projective dimension at most 1 whenever the related Gabriel filter of right ideals has a countable base. The other one is that a flat epimorphism of commutative rings has projective dimenension at most 1 whenever, in the related Gabriel filter of ideals, the quotient ring by any ideal in the filter is semilocal of Krull dimension zero. In both cases, the argument is based on certain computations with contramodules.

21.5. Jan Šťovíček (MFF UK): MACKEY ALGEBRAS WHICH ARE GORENSTEIN

14.5. Pooyan Moradifar (Tehran University): GORENSTEIN TILTING MODULES AND FINITISTIC DIMENSION CONJECTURES

30.4. Michal Hrbek (MU AVCR, Univ. Padova): COMPACTLY GENERATED T-STRUCTURES AND UNBOUNDED SILTING COMPLEXES

23.4. Alexander Slavik (MFF UK, Univ. Manchester): MODEL THEORY OF TORSION MODULES AND CONTRAMODULES

23.4. Andrii Gatalevych (Univ. Lviv): BEZOUT RINGS WITH NONZERO JACOBSON RADICAL AND SEMI-HEREDITARY BEZOUT RINGS.

16.4. Leonid Positselski (Univ. Haifa): QUADRATIC ALGEBRAS AND THEIR HILBERT SERIES

16.4. Andrii Gatalevych (Univ. Lviv): ELEMENTARY DIVISOR RINGS AND FINITELY PRESENTED MODULES. ADEQUATE RINGS AND THEIR GENERALIZATIONS.

9.4. Leonid Positselski (Univ. Haifa): AUSLANDER AND BASS CLASSES FOR SEMI-DUALIZING COMPLEXES, AND PSEUDO-DERIVED CATEGORY EQUIVALENCES

26.3. Anatoliy Dmytruk (Univ. Lviv): CLEAN DUO RINGS

5.3. Pavel Příhoda (MFF UK): PURE PROJECTIVE MODULES OVER NON-SINGULAR SERIAL RINGS

26.2. Roger Wiegand (Univ. Nebraska): BETTI TABLES OVER SHORT GORENSTEIN ALGEBRAS

19.2. Jan Šťovíček (MFF UK): FLAT EPIMORPHISMS FOR COMMUTATIVE NOETHERIAN RINGS

15.1. Yuriy Ishchuk (Univ. of Lviv): THE ZERO-DIVISORS GRAPHS OF FINITE RINGS AND MATRIX SEMIGROUPS
Abstract: A commutative ring R can be considered as a simple graph whose vertices are elements of R and two different elements x and y of R are adjacent if and only if xy=0. The idea of colouring of a commutative ring establishes a connection between graph theory and commutative ring theory which hopefully will turn out to be mutually beneficial for these two branches of mathematics. In a manner analogous to the commutative case, the zero-divisor graph of a non-commutative semigroup S can be defined as the directed graph \Gamma(S) whose vertices are all non-zero zero-divisors of S$ in which for any two distinct vertices x and y, x\to y is an edge if and only if xy=0. In the talk, we shall discuss the interplay between the properties of a matrix semigroup S over a finite ring R and the graph-theoretic properties of \Gamma(S), \Gamma(R): the connectedness, diameter, existence of sources, sinks, etc.

8.1. Yuriy Ishchuk (Univ. of Lviv): SEMIGROUPS AND S-POLYGONS WITH ANNIHILATION CONDITIONS
Abstract: The notions of semicommutative semigroup $S$ and abelian $S$-polygon ($S$-act) by analogy with the notions of semi commutative, abelian modules and rings will be introduced. The interdependences between reduced, reversible and semicommutative semigroups are investigated. It was proved that the class of abelian $S$-polygons is closed under subpolygons, direct products and homomorphic images. Using the notions of Baer's conditions for modules I will introduce p.p.-Baer $S$-polygons and prove that if $A_S$ is a p.p.-Baer $S$-polygon, then the conditions for $A_S$ to be a reduced, symmetric, semicommutative and an abelian $S$-polygon are equivalent.

2017

11.12. Jan Šťovíček (MFF UK): RECOGNIZING EXACTNESS OF DIRECT LIMITS FROM AN INJECTIVE COGENERATOR

4.12. Jan Šaroch (MFF UK): SIMSON'S MINIMAL COUNTEREXAMPLE TO THE PURE-SEMISIMPLICITY CONJECTURE REVISITED

27.11. Leonid Positselski (Univ. Haifa): STRONGLY FLAT MODULES W.R.T. SEVERAL MULTIPLICATIVE SUBSETS

20.11. Jakub Kopřiva (MFF UK): PULLBACKS OF FINITELY GENERATED ALGEBRAS OVER COMMUTATIVE NOETHERIAN RINGS
Abstract: The problem whether the pullback of two finitely generated algebras over a Noetherian commutative ring is finitely generated arises from the study of existence of pushouts of affine algebraic varieties. The problem can be easily reduced to asking when two types of subalgebras of a finitely generated algebra are finitely generated. In this talk, I will give a complete description of finitely generated subalgebras of one type and use it to show that some special subalgebras of the other type are finitely generated. I will also discuss local properties of said pullbacks and some examples from algebraic geometry.

13.11.Andrew Mathas (Univ. Sydney): THE REPRESENTATION THEORY OF THE SYMMETRIC GROUPS
slides

6.11. Leonid Positselski (Univ. Haifa): OBTAINABLE MODULES AND THE DESCENT OF VERY FLATNESS
Abstract: The proof of the very flat conjecture is based on the main lemmas describing descent properties of the class of very flat modules with respect to certain morphisms of commutative rings. The proofs of the main lemmas are, in turn, based on a combination of three techniques: obtainable modules, contramodules, and a derived category version of the Nunke-Matlis exact sequence. In this talk, I will explain what obtainable modules are and how to use them, and sketch the proofs of the two main lemmas. Time permitting, I may also say a few words about the generalization of some results about very flatness to strongly flat and weakly cotorsion modules.

30.10.Andrew Mathas (Univ. Sydney): JANTZEN FILTRATIONS AND GRADED SPECHT MODULES
Abstract: The Jantzen sum formula is a classical result in the representation theory of the symmetric and general linear groups that describes a natural filtration of the Specht modules over any field. Analogues of this result exist for many algebras including the cyclotomic Hecke algebras of type A. Quite remarkably, the cyclotomic Hecke algebras of type A are now know to admit a Z-grading because they are isomorphic to cyclotomic KLR algebras. I will explain how to give an easy proof, and stronger formulation, of Jantzen sum formula for the cyclotomic Hecke algebras of type A using the KLR grading. I will discuss some consequences and applications of this approach.

23.10. (15:30) Leonid Positselski (Univ. Haifa): THE VERY FLAT CONJECTURE IN COMMUTATIVE ALGEBRA
Abstract: The very flat conjecture claims that any flat, finitely presented commutative algebra over a commutative ring is a very flat module over that ring. This was formulated in February 2014 and proved in the Summer of 2017. In the talk, I will introduce two formulations of the conjecture and discuss corollaries. Then I will formulate two versions of the Main Lemma and deduce the conjecture from the Main Lemma. Time permitting, I will also say a few words about the proofs of (at least some versions) of the Main Lemma, and about its extensions from the very flat to the strongly flat/quite flat setting.

23.10. (16:30) Simone Virili (Univ. Murcia): FACTORIZATION SYSTEMS ON (STABLE) DERIVATORS
Abstract

16.10. Jan Nekovář (Univ. Pierre et Marie Curie, Paris): WHAT CAN ONE SAY ABOUT A REPRESENTATION OF A GIVEN GROUP OR ALGEBRA, IF IT IS A ROOT OF THE CHARACTERISTIC POLYNOMIAL OF A TENSOR PRODUCT OF SEVERAL IRREDUCIBLE REPRESENTATIONS OF THE SAME GROUP OR ALGEBRA?

2.10. Zahra Nazemian (IPM Tehran): ISOARTINIAN AND ISONOETHERIAN MODULES AND RINGS

25.9. Alberto Facchini (Univ. Padova): UNIQUENESS OF DECOMPOSITIONS AND FACTORIZATIONS, G-GROUPS AND POLYNOMIALS

26.6. Leonid Positselski (Univ. Haifa): ALMOST PERFECT MULTIPLICATIVE SUBSETS IN COMMUTATIVE RINGS

20.6. Leonid Positselski (Univ. Haifa): ABELIAN RIGHT PERPENDICULAR SUBCATEGORIES IN MODULE CATEGORIES 3

12.6. Leonid Positselski (Univ. Haifa): ABELIAN RIGHT PERPENDICULAR SUBCATEGORIES IN MODULE CATEGORIES 2

5.6. Leonid Positselski (Univ. Haifa): ABELIAN RIGHT PERPENDICULAR SUBCATEGORIES IN MODULE CATEGORIES
Abstract: Geigle and Lenzing defined the perpendicular subcategories to classes of objects in abelian categories, and proved that the right perpendicular subcategory to a class of objects of projective dimension 1 is abelian. More generally, one can consider those Ext^{0,1}-perpendicular subcategories to classes of objects that just happen to be abelian with an exact inclusion functor, for whatever reason. In particular, if the Ext^{0,1}-perpendicular subcategory to a given class of objects happens to coincide with the Ext^{0,1,2}-perpendicular subcategory to the same objects, then this subcategory is abelian. In this talk I will suggest a series of definitions of perpendicular subcategories, and show that, no matter which one of these definitions one chooses, the class of abelian categories obtainable as the right perpendicular subcategories to sets of objects or morphisms in module categories turns out to be the same. Namely, it it the class of all locally presentable abelian categories with a projective generator.

22.5. Pavel Coupek: 1-COTILTING SHEAVES ON CURVES

15.5. Michael Lieberman (ECI): NONFORKING FOR THE REST OF US
Abstract: The related notions of nonforking, independence, and stable amalgamation are of central importance in the development of the stability theory of both elementary and nonelementary classes, but have not been much appreciated (or understood) by nonspecialists. We discuss ongoing joint work with Jiří Rosický and Sebastien Vasey, which aims to provide a friendlier, more straightforwardly mathematical, category-theoretic formulation of this idea. In particular, we develop a well-behaved nonforking relation for coregular locally presentable and locally multi-presentable categories. Time permitting, we will consider why the latter case may be very interesting, indeed.

24.4. Alessandro Rapa (Univ. Trento): ATOM SPECTRUM OF COTILTING HEARTS: KRONECKER CASE

10.4. Jan Šaroch (MFF UK): PROJECTIVELY RESOLVED GORENSTEIN FLAT MODULES ARE GORENSTEIN PROJECTIVE

3.4. Pavel Příhoda (MFF UK): CONSTRUCTIONS OF PURE PROJECTIVE MODULES OVER CHAIN DOMAINS

27.3. Jan Šťovíček (MFF UK): COTILTING SHEAVES ON NOETHERIAN SCHEMES

20.3. Aibat Yeskeyev (Qaraghandy State University named after E.A.Buketov): THE PROPERTIES OF JONSSON THEORIES AND THEIR MODELS

13.3. Jan Šaroch (MFF UK): DEFINABILITY, $\Sigma$-COTORSION MODULES AND SINGULAR COMPACTNESS

6.3. Alexander Slávik (MFF UK): DERIVED CATEGORIES OF CERTAIN SUBCATEGORIES OF FLAT SHEAVES

27.2. Samuel Mokriš (MFF UK): SOLUTION TO WEHRUNG'S PROBLEM ON BANASCHEWSKI FUNCTIONS

9.1. Alexander Slávik (MFF UK): VERY FLAT MODULES AND QUASI-COHERENT SHEAVES
The class of very flat modules over a commutative ring has many nice properties; for instance, the notion of very flatness is Zariski-local, therefore it makes perfect sense to define very flat quasi-coherent sheaves. The main idea is to use this class as a remedy for the lack of projective quasi-coherent sheaves, replacing the usual approach (due to Murfet) via flat sheaves. Joint work with S. Estrada and J. Trlifaj with occasional hints from L. Positselski.

2016

19.12. Magnus Hellstroem-Finnsen (NTNU Trondheim): HOCHSCHILD COHOMOLOGY OF MONOIDS
We define the Hochschild complex and cohomology of a monoid in an Ab-enriched monoidal category. Then we interpret some of the lower dimensional cohomology groups and discuss that the cohomology ring is to be graded-commutative.

12.12. Michal Hrbek (MFF UK): n-TILTING CLASSES AND LOCAL HOMOLOGY

5.12. Jan Trlifaj (MFF UK): ZARISKI LOCALITY FOR TILTING QC-SHEAVES OVER LOCALLY NOETHERIAN SCHEMES

28.11. Leonid Positselski (Univ. Haifa): \infty-TILTING AND CONTRAMODULES

21.11. Leonid Positselski (Univ. Haifa): TILTING-COTILTING CORRESPONDENCE

14.11. Tibor Beke (University of Massachussetts): ACCESSIBLE FUNCTORS AND LAMBDA-EQUIVALENT OBJECTS

7.11. Peter Vamos (University of Exeter): IMMEDIATE EXTENSIONS OF RINGS

31.10. Leonid Positselski (Technion): COTORSION MODULES OVER COMMUTATIVE NOETHERIAN RINGS OF KRULL DIMENSION 1

17.10. Amit Kuber (ECI Brno): K-THEORY OF MODEL-THEORETIC STRUCTURES

8.9. Pedro Guil Asensio (Univ. Murcia): EXACT CATEGORIES WITH DIRECT LIMITS

8.9. Sergio Estrada Dominguez (Univ. Murcia): VERY FLAT QUASI-COHERENT SHEAVES

23.5. Cihat Abdioglu (Karamanoglu Mehmetbey Univ.): CENTRALIZING MAPPINGS, DERIVATIONS AND FUNCTIONAL IDENTITIES IN PRIME RINGS

29.6. Pavel Čoupek (MFF): 1-COTILTING SHEAVES ON A NOETHERIAN SCHEME

16.5. Jan Šaroch (MFF): ON SOLVABILITY OF Z-LINEAR HOMOGENOUS EQUATIONS IN Z

9.5. Problem session on silting theory

25.4. Igor Kriz (University of Michigan in Ann Arbor): DERIVED REPRESENTATION THEORY

18.4. Ali Mahin Fallah (University of Isfahan): ON THE AUSLANDER-REITEN CONJECTURE FOR ALGEBRAS

4.4. Gennady Puninskyi (Belarusian State University): THE GERASIMOV-SAKHAEV EXAMPLE REVISITED.

21.3. Jan Šaroch (MFF): PREENVELOPING TORSION CLASSES AND PURE-PROJECTIVE MODULES

14.3. Michal Hrbek (MFF): n-TILTING MODULES OVER COMMUTATIVE RINGS

7.3. Pavel Příhoda (MFF): PURE PROJECTIVE TILTING MODULES

11.1. Manuel Saorín (Univ. Murcia) SILTING THEORY AND A TILTING THEORY FOR AB3 ABELIAN CATEGORIES

2015

21.12. Leonid Positselski (Technion & IITP) CONTRAHERENT COSHEAVES 4

15.12. Leonid Positselski (Technion & IITP) CONTRAHERENT COSHEAVES 3

14.12. Moritz Groth (MPIM Bonn) CHARACTERIZATIONS OF STABILITY FOR ABSTRACT HOMOTOPY THEORIES

7.12. Leonid Positselski (Technion & IITP) CONTRAHERENT COSHEAVES 2

30.11. Leonid Positselski (Technion & IITP) CONTRAHERENT COSHEAVES

23.11. Pavel Příhoda (MFF): DOMAINS WITH FULLY DECOMPOSABLE GENERALIZED LATTICES

16.11. Jan Trlifaj (MFF): R-PROJECTIVITY

13.11. Roger Wiegand (Univ. Nebraska) MODULES WITH NO SELF-EXTENSIONS
Let R be a local Noetherian Gorenstein domain, and let M be a finitely generated R-module such that M\otimes_R M^* is maximal Cohen-Macaulay. The so-called "Huneke-Wiegand Conjecture" (from the early nineties) asserts that M must be a free module. The conjecture reduces to the one-dimensional case, where it can be shown (assuming, harmlessly, that M is torsion-free) that the torsion submodule of M\otimes_R M^* is Ext^1_R(M,M). Thus the conjecture asserts that over a local one-dimensional Gorenstein domain every rigid module (a module for which every self-extension splits) is free. The conjecture is open even when R is a complete intersection and M is an ideal of R. In work with Srikanth Iyengar and Craig Huneke, we have verified many cases of the conjecture, for example, when M is a licci ideal of R.

2.11. Leonid Positselski (Technion & IITP) COTORSION THEORIES IN LOCALLY PRESENTABLE ABELIAN CATEGORIES
I will explain how to apply a small object argument-based approach to the construction of complete cotorsion theories in locally presentable abelian categories, partially generalizing the work of Eklof and Trlifaj. This technique can be applied in order to deduce completeness of the flat and very flat cotorsion theories in the categories of contramodules over the topological projective limit of a sequence of associative (resp., commutative) rings. I will also present a counterexample showing why a full generalization of the Eklof-Trlifaj theorem to locally presentable abelian categories does not seem to be possible. Time permitting, I may also say a few words about a proof of the existence of flat covers in contramodule categories. The talk is based on a recent joint work with J. Rosicky.

26.10. Michal Hrbek (MFF): SILTING OVER COMMUTATIVE RINGS

19.10. Vitezslav Kala (MFF): FINITELY GENERATED LATTICE-ORDERED GROUPS

12.10. Jan Stovicek (MFF): SILTING RING EPIMORPHISMS ARE OF COUNTABLE TYPE

23.6. Philipp Rothmaler (CUNY New York) MITTAG-LEFFLER MODULES

2.6. Markus Schmidmeier (Florida Atlantic Univ.) A SWISS CHEESE THEOREM FOR LINEAR OPERATORS WITH TWO INVARIANT SUBSPACES
In this talk we discuss a joint project with Audrey Moore on the possible dimension types of linear operators with two invariant subspaces. Formally, we consider systems $(V, T, U_1, U_2)$ where $V$ is a finite dimensional vector space, $T: V\to V$ a nilpotent linear operator, and $U_1$, $U_2$ subspaces of $V$ which are contained in each other and which are invariant under the action of $T$. To each system we can associate the dimension type $(\dim U_1, dim U_2/U_1, dim V/U_2)$.
Such systems occur in the theory of linear time-invariant dynamical systems where the subquotient $U_2/U_1$ is used to reduce the dynamical system to one which is completely controllable and completely observable.
No gaps but holes: The well-known No-Gap Theorem by Bongartz states that for a finite dimensional algebra over an algebraically closed field, whenever there is an indecomposable module of length $n>1$, then there is one of length $n-1$. By comparison, consider the space given by the dimension types of indecomposable systems in the situation where $T$ acts with nilpotency index at most 4. Our main result states that in this space there are triples, for example $(3,1,3)$, which can not be realized as the dimension type of an indecomposable object, while each neighbor can.

18.5. Jan Šťovíček (MFF): UNIVERSAL LOCALIZATIONS, TORSION CLASSES, AND TAU-TILTING THEORY

11.5. Ivo Herzog (Ohio State Univ.): REPRESENTATION THEORY OF THE DUBROVIN-PUNINSKI RING

4.5. Michal Hrbek (MFF): TILTING AND COFINITE-TYPE COTILTING OVER COMMUTATIVE RINGS

27.4. Alexander Slávik (MFF): CONTRAADJUSTED MODULES OVER DEDEKIND DOMAINS

13.4. Jan Šaroch (MFF): MITTAG-LEFFLER MODULES AND RIGHT ALMOST SPLIT MAPS

23.3. Pavel Příhoda (MFF): PURE-PROJECTIVE MODULES OVER COMMUTATIVE RINGS

9.3. Jan Trlifaj (MFF): VERY FLAT AND LOCALLY VERY FLAT MODULES

2.3. Michal Hrbek (MFF): TILTING IN ONE-DIMENSIONAL DOMAINS

23.2. Ivo Herzog (Ohio State Univ.): PURE-SEMISIMPLE CONJECTURE

2014

15.12. Christmas party

1.12. Jan Šťovíček (MFF): ON PURITY AND APPLICATIONS TO CODERIVED AND SINGULARITY CATEGORIES

25.11. Siamak Yassemi (IPM Tehran & MPI Bonn): A THEOREM OF BASS: PAST, PRESENT, AND FUTURE

24.11. Siamak Yassemi (IPM Tehran & MPI Bonn): COMBINATORIAL ASPECTS OF COMMUTATIVE ALGEBRA
In 1975 a new trend of commutative algebra arose with the work by Richard Stanley who used the theory of Cohen-Macaulay rings to prove affirmatively the upper bound conjecture for spheres. It then turned out that commutative algebra supplies basic methods in the algebraic study of combinatorics on convex polytopes and simplicial complexes. Stanley was the first who used in a systematic way concepts and technique from commutative algebra to study simplicial complexes by considering the Hilbert function of Stanley-Reisner rings, whose defining ideals are generated by square-free monomials. Since then, the study of square-free monomial ideals from both the algebraic and combinatorial point of view is one of the most exciting topics in commutative algebra.
In this talk we present a survey on some research on combinatorial commutative algebra.

11.11. Roger Wiegand (Univ. of Nebraska, Lincoln): NON-UNIQUENESS OF DIRECT SUM DECOMPOSITIONS (abstract)

10.11. (15:30) Roger Wiegand (Univ. of Nebraska, Lincoln): VANISHING OF TOR OVER COMPLETE INTERSECTIONS (abstract)

10.11. (16:20) Sylvia Wiegand (Univ. of Nebraska, Lincoln): BUILDING EXAMPLES USING POWER SERIES OVER NOETHERIAN RINGS
Joint work with William Heinzer and Christel Rotthaus
In ongoing work with William Heinzer and Christel Rotthaus over the past twenty years we have been applying a construction technique for obtaining sometimes baffling, sometimes badly behaved, sometimes Noetherian, sometimes non- Noetherian integral domains. This technique of intersecting fields with power series rings goes back to Akizuki-Schmidt in the 1930s and Nagata in the 1950s, and since then has also been employed by Nishimuri, Heitmann, Ogoma, the authors and others.
We are writing a book about our procedures and examples. We present some of the theory and techniques we use, and mention some examples. In particular we may mention some famous classical examples and show how they are streamlined with this technique or give an example that is "almost Noetherian" in that exactly one prime ideal is not finitely generated.

10.11. (17:10) Ciprian Modoi (Babes-Bolyai Univ., Cluj-Napoca): IDEAL COTORSION PAIRS IN TRIANGULATED CATEGORIES I

10.11. (18:00) Simion Breaz (Babes-Bolyai Univ., Cluj-Napoca): IDEAL COTORSION PAIRS IN TRIANGULATED CATEGORIES II

3.11. Michael Lieberman (ECI): CLASSIFICATION THEORY FOR ACCESSIBLE CATEGORIES
We discuss recent joint work with Jiří Rosický which seeks to extend a fragment of the classification theory of AECs to the more general framework of accessible categories, particularly for accessible categories with concrete directed colimits: essentially AECs minus coherence. There are several pleasant surprises---a generalization of Boney's recent theorem on tameness of AECs under a large cardinal hypothesis follows from work of Makkai and Paré. On the other hand, these categories admit a robust Ehrenfeucht-Mostowski functor which can be used to mimic certain constructions in AECs, which should have new and meaningful implications in categorical algebra.

31.10. Moritz Groth (MPI, Bonn): INTRODUCTION TO \INFTY-CATEGORIES

20.10. Pavel Příhoda (MFF UK): TRACE IDEAL OF A PURE PROJECTIVE MODULE

13.10. Jan Šťovíček (MFF UK): HIGHER TRIANGULATIONS AND MAY'S AXIOMS AS CONSEQUENCES OF REPRESENTATION THEORY

6.10. Jan Šaroch (MFF UK): RELATING DIRECT SUMS AND DIRECT PRODUCTS OF THE REGULAR MODULE

5.6. Xianhui Fu (Northeast Normal University, Changchun, China): THE MONO-EPI EXACT SUBSTRUCTURE OF THE CATEGORY OF ARROWS AND ITS APPLICATIONS
The mono-epi (ME) exact structure on the morphisms of an exact category (A;E) is introduced. The ideal versions of Eklof's Lemma and Eklof-Trlifaj's Lemma will be shown in this talk. The ideal version of Eklof's Lemma will be applied to prove the following result: if R is a left coherent ring, then the category of pure-projective left R-modules is closed under extensions if and only if every FP-projective left R-module is pure-projective.

26.5. ECI ALGEBRA DAY (from 11am in lecture theatre K1)
A joint workshop of the ECI algebra groups from Brno and Prague on open problems, presented by J.Bourke (MU Brno), P.Prihoda (MFF UK), L.Vokrinek (MU Brno), M.Korbelar (MU Brno), J.Stovicek (MFF UK), J.Rosicky (MU Brno) and J.Trlifaj (MFF UK)

5.5. Jan Šaroch (MFF UK): ORDERED FIELDS, THEIR INTEGER PARTS, AND INDUCTION

14.4. Jan Trlifaj (MFF UK): APPROXIMATIONS VS. GENERALIZED INJECTIVITY

31.3. Leonid Positselski (Univ. Bielefeld & NRUHSE Moscow): CONTRAMODULES AND CONTRAHERENT COSHEAVES
Contramodules are a wide class of module-type algebraic structures endowed with infinite summation operations. Defined originally by Eilenberg and Moore in 1965 in the case of coalgebras over commutative rings, they experience a small renaissance now after being all but forgotten for three or four decades. I will define contramodules over topological rings, some topological Lie algebras, and topological groups, and discuss contramodules over compele Noetherian rings in some detail. Globalizing contramodules over nonaffine algebraic varieties requires the notion of a contraherent cosheaf, and I will say a few words about these, too.

24.3. Michal Hrbek (MFF UK): MINIMAL GENERATION OF ABELIAN GROUPS AND MODULES
We present a work in progress, which can be motivated by the following question: Which abelian groups have the property that any set of generators contains a minimal set of generators (minimal with respect to inclusion)? The main obstacle to answering this leads to a question concerning a characterization of perfect rings asked in a paper by Nashier and Nichols from 1991, and innocent as it may look, it seems to be open. Although so far we are unable to provide an answer, we solve several intermediate problems, which have nice linear algebraic or even combinatorial formulations. (Joint work with D. Herden and P. Růžička.)

10.3. Adam-Christiaan van Roosmalen (MFF UK): HALL ALGEBRAS FOR REPRESENTATIONS OF LINEARLY ORDERED SETS
This talk is based on joint research with Qunhua Liu and Guillaume Pouchin. Let Q be a quiver of Dynkin type A and let F_q be a finite field with q elements. It is well-known that the Hall algebra of the category of F_q representations of Q is connected with the quantized enveloping algebra of sl(n). In this talk, I will replace the quiver Q by an infinite linearly ordered set and describe the corresponding Hall algebra. This algebra can then be seen as a quantization of the positive part of the enveloping algebra of a locally finite Lie algebra.

24.2. Daniel Herden (MFF UK): BLACK BOXES FOR ALEPH_2-FREE GROUPS

14.1. Mauritz Groth (Radboud Univ. Nijmegen) : TILTING THEORY VIA STABLE HOMOTOPY THEORY
Tilting theory is a derived version of Morita theory. In the context of quivers Q and Q' and a field k, this amounts to looking for conditions which guarantee that the derived categories of the path algebras D(kQ) and D(kQ') are equivalent as triangulated categories. In this project (which is j/w Jan Stovicek) we take a different approach to tilting theory and show that some aspects of it are formal consequences of stability. Slightly more precisely, we show that certain tilting equivalences can be lifted to the context of arbitrary abstract stable homotopy theory. Plugging in specific examples this tells us that refined versions of these tilting results are also valid over arbitrary ground rings, for quasi-coherent modules on a scheme, in the differential-graded context and also in the spectral context.

13.1. Andrew Mathas (Univ. Sydney): THE RISE AND FALL OF THE JAMES AND LUSZTIG CONJECTURES
Much of the activity in the representation theory of Lie groups in the last thirty years has been geared towards proving the James conjecture (type A) and the Lusztig conjecture (all types). Roughly speaking, these conjectures say that in certain circumstances the formal characters of the finite groups of Lie type coincide with the characters of corresponding irreducible representations for quantum groups at roots of unity. The characters of the irreducible representations of quantum groups at roots of unity are determined by certain (parabolic) Kazhdan-Lusztig polynomials so they are, in principle, completely known and understood. I will give a survey about the current status of these two conjectures.

6.1. Jan Trlifaj (MFF UK): SAORIN'S PROBLEM

2013

2.12. Daniel Herden (MFF UK): SOME ASPECTS OF \ALEPH_K-FREENESS

25.11. Jan Stovicek (MFF UK): TILTING IN STABLE HOMOTOPY THEORIES
The concept of a tilting module originated from Bernstein-Gelfand-Ponomarev reflection functors. Curiously, the reflection functors themselves have an easy interpretation in any reasonable stable homotopy theory and induce equivalences in this vastly generalized setting. The aim of the talk, which is based on recent joint work with Moritz Groth, is to explain this story.

18.11. Frederick Marks (Univ. Stuttgart) UNIVERSAL LOCALISATIONS AND TILTING MODULES FOR HEREDITARY RINGS
We study the interplay between universal localisations, as defined by Cohn and Schofield, and tilting modules in the context of hereditary rings. For finite dimensional algebras, we establish a bijection between finitely generated support tilting modules and finite dimensional universal localisations. As a consequence, the finitely generated tilting modules do all arise from universal localisation. This phenomenon is well known not to hold for arbitrary tilting modules over hereditary rings. Nevertheless, the methods involved in the classical setup allow us to find new criteria to decide whether a (possibly large) tilting module over a hereditary ring arises from localisation. This new approach, based on work in progress with Lidia Angeleri Huegel and Jorge Vitoria, will be discussed in the last part of the talk.

7.11. Sylvia Wiegand (University of Nebraska) : PRIME IDEALS IN NOETHERIAN POLYNOMIAL AND POWER SERIES INTEGRAL DOMAINS
Joint work with Ela Celikbas and Christina Eubanks-Turner
About sixty years ago, Irving Kaplansky asked the difficult question: "What partially ordered sets occur as the set of prime ideals of a Noetherian ring, ordered under inclusion?" Motivated by his question, we describe the set of prime ideals of mixed polynomial-power series rings of the form B = R[[x]][y]/Q, R[y][[x]]/Q or R[[x]][[y]]/Q, where R is a one-dimensional Noetherian domain, x and y are indeterminates, and Q is a height-one prime ideal of the appropriate ring with x \notin Q. Actually Spec(R[[x]][[y]]/Q) is somewhat easily characterized; and Spec(R[y][[x]]/Q) is similar to Spec(R[[x]][y]/Q). If R is a countable domain, our descriptions of Spec(R[y][[x]]/Q) and Spec(R[[x]][[y]]/Q) are characterizations.
If R is a countable one-dimensional domain with infinitely many maximal ideals, our possible descriptions for the partially ordered set Spec(R[[x]][[y]]/Q) can all be realized as Spec(Z[[x]][y]/Q), for an appropriate height-one prime ideal Q of Z[[x]][y], the mixed power series over the integers Z. We give some ideas of the proof using some counting techniques and an interesting property of Spec(Z[y]) observed by R. Wiegand in 1988. If time permits we may prove or discuss the partially ordered set SpecB, if R is a countable semilocal domain or if R is a Henselian ring.

7.11. Roger Wiegand (University of Nebraska) : TORSION IN TENSOR PRODUCTS AND VANISHING OF TOR
abstract

4.11. Hans C. Herbig (ECI) : OPEN AND SOLVED PROBLEMS IN SINGULAR POISSON GEOMETRY
I will talk about applications of the BFV-complex to deformation quantization of singular symplectic quotients. I will indicate why it is necessary to develop a cohomology theory for Lie-Rinehart pairs (A,L) that encompasses also the case when the the A-module underlying the Lie algebra L is non-projective.

21.10. Simion Breaz (Babes-Bolyai Univ., Cluj-Napoca): SUBGROUPS WHICH ADMIT EXTENSIONS OF HOMOMORPHISMS

21.10. Ciprian Modoi (Babes-Bolyai Univ., Cluj-Napoca): ON A THEOREM OF G. BERGMAN

7.10. Jan Saroch (MFF UK): RELATIVE MITTAG-LEFFLER MODULES AND PURE-INJECTIVITY

16.9. Lidie Angeleri (Univ. Verona): MODULES OF IRRATIONAL SLOPE OVER TUBULAR ALGEBRAS
We discuss the notion of slope over a canonical algebra of tubular type and focus on the modules of irrational slope. They are all infinite dimensional, and it turns out that they are determined by a tilting module, or dually, by a cotilting module. This also leads to classification results for indecomposable pure-injective modules.

15.8. Igor Kriz: SUPER-MODULAR FUNCTORS AND THEIR K-THEORETIC REALIZATIONS

15.7. John Baldwin (Univ. Illinois, Chicago): COMPLETENESS AND CATEGORICITY (IN POWER): FORMALIZATION WITHOUT FOUNDATIONALISM
This investigation arose as a contrast between the role of formal methods in usual model theory and what one might term ‘formalism-free’ methods in the study of AEC. Formalization has three roles: 1) a foundation for an area (perhaps all) of mathematics, 2) a resource for investigating problems in ‘normal’ mathematics, 3) a tool to organize various mathematical areas so as to emphasize commonalities and differences. We focus on the use of theories and syntactical properties of theories in roles 2) and 3). Formal methods enter both into the classification of theories and the study of definable set of a particular model. We regard a property of a theory (in first or second order logic) as virtuous if the property has mathematical consequences for the theory or for models of the theory. We argue that for second order logic, ‘categoricity’ of a theory (as opposed to categoricity of a specific axiomatization) has little virtue. For first order logic, categoricity is trivial. But ‘categoricity in power’ illustrates the sort of mathematical consequences we mean. One can lay out a schema with a few parameters (depending on the theory) which describes the structure of any model of any theory categorical in uncountable power. Similar schema for the decomposition of models apply to other theories according to properties defining the stability hierarchy. We describe arguments using properties, which essentially involve formalizing mathematics, to obtain results in ‘mainstream’ mathematics. We consider discussions on method by Kashdan, and Bourbaki as well as such logicians as Hrushovski and Shelah.

27.5. Pavel Paták (MFF UK): STRONG ASPECTS OF Z_2 HOMOLOGY

20.5. Zuzana Safernová POLYNOMIAL PARTITIONING METHOD IN DISCRETE GEOMETRY

14.5. Moritz Groth (Radboud Univ.): STABLE GROTHENDIECK DERIVATORS AND CANONICAL TRIANGULATIONS
The theory of derivators (going back to Grothendieck, Heller, and others) provides an axiomatic approach to homotopy theory. It adresses the problem that the rather crude passage from model categories to homotopy categories results in a serious loss of information. In the stable context, the typice defects of triangulated categories (non-functoriality of cone constru-ction, lack of homotopy colimits) can be seen as a reminiscent of this fact. The simple but surprisingly powerful idea behind a derivator is that instead one should form homotopy catego-ries of various diagram categories and also keep track of the calculus of homotopy Kan extensions.
In this talk we cover some basics of derivators culminating in a sketch proof that stable derivators provide an enhancement of triangulated categories. Possibly more important than this result itself are the techniques developed along the way as they lay the foundations for further research directions. The aim of this talk is to (hopefully) advertise derivators as a convenient, 'weakly terminal' approach to axiomatic homotopy theory.

13.5. Jan Šťovíček (MFF UK & ECI) HOMOLOGICAL EPIMORPHISMS FROM VALUATION DOMAINS

29.4. Jan Trlifaj (MFF): TOR-PAIRS

22.4. Pavel Růžička (MFF): WEAK BASES OF MODULES

18.3. Jan Trlifaj (MFF): COTILTING FOR COMMUTATIVE RINGS AND LOCALIZATION

11.3. Jan Šťovíček (MFF & ECI): TTF TRIPLES IN TRIANGULATED CATEGORIES II

4.3. Jan Šťovíček (MFF & ECI): TTF TRIPLES IN TRIANGULATED CATEGORIES

25.2. Jan Trlifaj (MFF): WILDNESS VERSUS PURE-SEMISIMPLICITY

17.1. Jan Šťovíček (MFF & ECI): DG ALGEBRAS AND EQUIVALENCE OF DERIVED CATEGORIES

15.1. Dolors Herbera (UA Barcelona): DEFINABLE CLASSES AND MITTAG-LEFFLER CONDITIONS

14.1. Michal Hrbek (MFF UK): MODULES WITH A MINIMAL GENERATING SET

7.1. Jan Stovicek (MFF UK): STABLE DERIVATORS, TORSION PAIRS IN TRIANGULATED CATEGORIES, AND A CLASSIFICATION OF CO-T-STRUCTURES
I will introduce stable derivators, a rather technical but interesting concept due to Grothendieck. I will outline how this can be used to study the structure of compactly generated torsion pairs in triangulated categories and to classify compactly generated co-t-structures in triangulated categories.

2012

19.12. Vítězslav Kala (MFF UK and Purdue University): ASYMPTOTIC RESULTS IN THE LANGLANDS PROGRAM
The Langlands program is a series of conjectures that provide a common framework for a large part of modern number theory. Its goal is to relate representations of absolute Galois groups of number fields to certain analytic objects, automorphic representations. For example, a special case of this correspondence was proved by Wiles and Taylor as the main step of the proof of Fermat's Last Theorem.
In the talk, we will first give an overview and a motivation for the Langlands program, keeping the prerequisited minimal. Then we will discuss some recent asymptotic results on the number of various types of Galois and automorphic representations.

17.12. Sylvia Wiegand (University of Nebraska): PRIME IDEALS IN NOETHERIAN RINGS
Let R be a commutative Noetherian ring. We consider the set Spec(R) of prime ideals of R as a partially ordered set, ordered by inclusion. Around 1950 Irving Kaplansky asked, "Which partially ordered sets arise as Spec(R) for some Noetherian ring R?" This question is completely open, even if only two-dimensional sets are considered, despite a large amount of work over the intervening years by many mathematicians, such as Hochster, Heitmann, Nagata, McAdam, and Ratli . In this talk, we describe prime spectra for some two-dimensional rings of polynomials and power series. This involves our work and work of William Heinzer, Christel Rotthaus, Roger Wiegand and our students.

10.12. Tibor Beke (University of Massachusets): A FUNCTORIAL VERSION OF SHELAH'S SINGULAR COMPACTNESS
Shelah's celebrated singular compactness theorem asserts that if G is a group whose cardinality is singular, and all subgroups of G are free, then G itself is free. Shelah's proof can be adapted to various other settings, including abelian groups, R-modules, filtered R-modules, colorings of infinite graphs, and transversals of systems of sets. It hasn't been clear whether there is a single statement unifying these applications and their various conclusions. This talk is a preliminary report on joint work with J. Rosicky on what seems to be the "most comprehensive" form of singular compactness. The proof is an adaptation of one of Shelah's arguments to the setting of accessible categories and functors.

3.12. Jan Saroch (MFF UK): COSTA'S CONJECTURE

26.11. Martin Doubek (MFF UK): ALGEBRAIC STRUCTURES IN STRING THEORY

12.11. Michael Lieberman (ECI): CATEGORIAL ABSTRACT MODEL THEORY
We outline the basic project of abstract model theory, and introduce abstract elementary classes (AECs), which recommend themselves as an ideal context in which to investigate generalized classi-fication theory. We consider the ways in which they represent a shift in the direction of category theory, leading to the peculiar no-mans-land between abstract model theory and accessible categories currently being explored by T. Beke, J. Rosicky, and myself. Finally, we consider a few surprising results concerning AECs that arise as simple appli-cations of ideas from the realm of accessible categories.

5.11. Pierre Schapira (Paris VI): ALGEBRAIC MICROLOCAL ANALYSIS I CHARACTERISTIC VARIETY AND MICROSUPPORT
On a complex manifold X, a coherent D-module M admits a characteristic variety char(M), a closed conic co-isotropic complex subvariety of the cotangent bundle T^*X. On a real manifold M, a sheaf admits a micro-support SS(F), a closed conic co-isotropic subset of the cotangent bundle T^*M. In this talk, I will explain both constructions, describe their functorial properties, and explain their links.

29.10. Pavel Příhoda (MFF UK): PURE PROJECTIVE MODULES OVER CHAIN DOMAINS WITH KRULL DIMENSION

15.10. David Pospisil (ECI): A CLASSIFICATION OF COMPACTLY GENERATED CO-T-STRUCTURES FOR COMMUTATIVE NOETHERIAN RINGS
We classify compactly generated co-t-structures in derived categories of commutative noetherian rings using a recent result of Alonso, Jeremias and Saorin. We also show that the collection of co-t-structures admitted by the category of perfect complexes is very restricted (joint work with J.Šťovíček).

8.10. Jan Triflaj (MFF UK): APPROXIMATIONS AND LOCALLY FREE MODULES
In 2003 Shelah set the first limits to approximation theory by showing independence of Whitehead groups being a precovering class. Recently, flat Mittag-Leffler modules over countable non-perfect rings were shown not to form a precovering class in ZFC.
We find a different proof of the latter fact which, combined with infinite dimensional tilting theory, makes it possible to trace the phenomenon to all countable hereditary artin algebras R of infinite representation type: We prove that the class of all locally Baer R-modules is not precovering (joint work with A.Slávik).

27.6. Ivo Dell'Ambrogio (Univ. Regina, Canada): A HOMOTOPICAL LOOK AT CLASSICAL MORITA THEORY
Quite recently, Gonçalo Tabuada and I have noticed a rather amusing little fact: there is a very nice Quillen model structure on the category of small preadditive categories, such that two rings become isomorphic in its homotopy category if and only if they are Morita equivalent, in the usual sense. Even better, we can use this to provide conceptual links on Morita equivalence, Picard groups, the Grothendieck group and (working relative to a base commutative ring) the notion of Azumaya algebra.

25.6. Greg Stevenson (Univ. Bielefeld): CLASSIFICATION PROBLEMS FOR TRIANGULATED CATEGORIES

14.5. Jan Šťovíček (MFF UK): 2-CALABI-YAU CATEGORIES WITH A CLUSTER TILTING SUBCATEGORY

23.4. Jan Šťovíček (MFF UK): INFINITE CLUSTER CATEGORIES
Based on joint work with Adam-Christiaan van Roosmalen, I will present a class of examples of triangulated categories with a cluster tilting subcategory containing infinitely many indecomposable objects. Among these, there is a class of categories of infinite Dynkin type A, which admit a rather simple combinatorial description.

16.4. Alexander Kazda (MFF UK): USING ABSORBTION ON REFLEXIVE DIGRAPHS
We show new, shorter, proofs for some known results about algebras of operations on reflexive digraphs.

2.4. Adam-Christiaan van Roosmalen (Univ. Regina, Canada): T-STRUCTURES FOR HEREDITARY CATEGORIES

26.3. Jan Trlifaj (MFF UK): P-ADIC MODULES VERSUS UNIVERSAL MAPS (STRUCTURE OF 1-COTILTING MODULES OVER COMMUTATIVE NOETHERIAN RINGS)

19.3. Jan Šťovíček (MFF UK): TRIANGULATED QUOTIENTS OF THE DERIVED CATEGORY OF A VALUATION DOMAIN

5.3. Jan Trlifaj (MFF UK): TREE MODULES AND MITTAG-LEFFLER CONDITIONS

20.2. Luigi Salce (Univ. Padova): BICAN-GROUPS (ON THE OCCASION OF THE 70TH BIRTHDAY OF LADISLAV BICAN)

2011

19.12. Martin Markl (MU AVCR): DEFORMATIONS OF ALGEBRAS AND THEIR DIAGRAMS.
We will explain how to construct a cohomology theory governing deformations of algebras of specific types (associative, commutative, Lie, Poisson), and of diagrams of these algebras.
Our talk will emphasize the `practical' side and will focus on a `computational recipe' rather than an abstract theory. We will give many examples of deformation cohomology for algebras, morphisms of algebras and, more generally, diagrams of morphisms of algebras.

12.12. Jakub Bulín (MFF UK): ABSORBTION IN FINITE RELATIONAL STRUCTURES
The notion of absorbing subuniverse plays an increasingly important role in finite universal algebra and the algebraic approach to CSP. We will mention several applications of absorption and then discuss the following open problem: Given a finite relational structure A and a subset B of A, is it decidable if B is an absorbing subuniverse? We provide an affirmative answer in the case when A has bounded width (i.e., the algebra of polymorphisms of A generates a congruence meet-semidistributive variety). Our proof mimics the proof of Zadori's conjecture by Barto: the idea is to encode the problem as an instance of CSP(A).

5.12. Zbyněk Šír (MFF UK): CONSTRUCTIONS FOR PYTHAGOREAN HODOGRAPH CURVES

21.11. Alexandr Kazda (MFF UK): NEAR UNANIMITY IN POSETS AND GRAPHS

14.11. Jan Šaroch (MFF UK): ARONSZAJN TREES AND BERGMAN’S INVERSE SYSTEMS

31.10. Christopher C. Gill (MFF UK): TENSOR PRODUCTS OF YOUNG MODULES AND DECOMPOSITION NUMBERS FOR SYMMETRIC GROUPS

17.10. Jan Trlifaj (MFF UK): MAXIMAL COHEN-MACAULAY MODULES AND TILTING FOR REGULAR LOCAL RINGS
Hochster´s conjecture says that maximal Cohen-Macaulay modules exist over any complete local commutative noetherian ring. In 1973 the conjecture was proved for rings of Krull dimension at most 2, but it is still open in general.
Recently tilting classes over commutative noetherian rings have been classified in terms of specialization closed subsets of the Zariski spectrum and the Auslander-Bridger transpose.
In this talk we will show that existence of maximal Cohen-Macaulay modules yields an alternative description of the tilting classes, and derive some consequences for the structure of these modules using approximation theory.

4.8. Martin Zeman (Univ. California at Irvine, USA): ABSOLUTENESS OF THE CORE MODEL
Steel has proved that if there is no inner model with a Woodin cardinal then it is possible to constuct a canonical iner model, the core model, that reflects all information about large cardinals in the set theoretic universe. In a joint result with Caicedo we show that if M is any proper class innner model that interprets the cardinal successor function correctly on a proper class of regular cardinals, then M is able to figure out the core model, modulo some random information. We also give local version of the result and an application in descriptive set theory.

30.6. Frantisek Marko (Pen. State, Hazelton, USA): BIDETERMINANTS FOR SCHUR SUPERALGEBRAS

29.6. Alexander Zubkov (Omsk State Ped. Univ., Omsk, Russia): PSEUDOCOMPACT QUASI-HEREDITARY ALGEBRAS

29.6. Alex Martsinkovsky (North Eastern Univ., Boston, USA): 1-TORSION AND HORIZONTAL LINKAGE OF FINITE MODULES OVER SEMIPERFECT RINGS

27.5. Phill Schultz (Univ. Western Australia, Perth): DUALITIES FOR SELF-SMALL GROUPS
I use a class of dualities to describe the structure of mixed abelian groups G satisfying two finiteness conditions:
1. G has finite rank, i.e., G contains a free subgroup of maximal finite dimension;
2. G is self-small, i.e., the image of every homomorphism from G into a countable direct sum of copies of G is contained in finitely many of these copies.
(Joint work with S.Breaz).

23.5. Pavel Goralčík (Université de Rouen): EQUIMORPHIC DIVERSITY
The talk will address, for a variety of categories, the question of the numer of non-isomorphic objects that have isomorphic monoids of endomorphisms (joint work with M.Demlová and V.Koubek).

16.5. Jan Trlifaj (MFF UK): PURE CHAINS AND MITTAG-LEFFLER MODULES

12.5. David Pospíšil (MFF UK): CLASSIFICATION OF TILTING AND COTILTING CLASSES FOR COMMUTATIVE NOETHERIAN RINGS

2.5. Ruediger Goebel (Universitaet Duisburg-Essen): ABSOLUTELY RIGID FIELDS

18.4. Pierre Gillibert (ECC): CRITICAL POINTS BETWEEN STRONGLY CONGRUENCE-PROPER VARIETIES OF ALGEBRAS

11.4. Gabor Braun (Univ. Duisburg-Essen): PATHOLOGICAL DUAL GROUPS UNDER MARTIN'S AXIOM
Under Martin's axiom, the Baer--Specker group, Z^{\omega} has a large supply of dual groups, ie, groups of the form Hom(A,Z). These provide many pathological examples found by several authors. Eg, for every non-negative integer k, there is a reflexive group G, with G \cong G \oplus Z^n if and only if k divides n. There is also a group A whose nth dual is not an (n+1)st dual for all n.
All these are variations of the same construction, namely, a standard method to represent endomorphism rings adapted to dual groups. I will explain this technique, so the audience will be able to come up with its own pathological dual groups. Only basic knowledge of abelian groups is required to understand the lecture.

28.3. Jan Šťovíček (MFF UK): PROJECTIVE MODULES OVER NON-NOETHERIAN SEMILOCAL RINGS
In the talk, I will discuss a classification of tilting and cotilting classes over commutative noetherian rings, recently obtained jointly with Lidia Angeleri, David Pospisil and Jan Trlifaj. The classification is in terms of certain subsets of the Zariski spectrum of the corresponding ring.
To give a context, the tilting and cotilting modules in the talk are generalized infinitely generated versions of classical finite dimensional tilting and cotilting modules from representation theory. The main application of classical (co)tilting modules is that they give a precise description of homological similarities between different algebras (in terms of so-called derived equivalences). Although one can to some extent generalize these results even to our setting, the corresponding theory is in its infancy and will be mentioned only marginally. I will rather focus on the classification and some examples.

21.3. Pavel Příhoda (MFF UK): PROJECTIVE MODULES OVER NON-NOETHERIAN SEMILOCAL RINGS
It would be nice to understand the behavior of projective modules over a general ring. In general, it is not possible - for example any reduced monoid with an order unit can express a direct sum decompositions of finitely generated projective modules over a suitable ring. Even for some very classical examples it is not easy to give a classification of projective modules - for integers in number fields it means exactly to determine its ideal class groups.
For semilocal rings, the situation is rather different. K_0 of a semilocal ring was determined in the 90's by A. Facchini and D. Herbera. D. Herbera and I obtained a similar result for countably generated projective modules over noetherian semilocal rings. But the non-noetherian case is still not understood well. In this talk I will discuss examples (mostly due to D. Herbera) that can be obtained using pullbacks and a remarkable example of Gerasimov and Sakhaev - a semilocal ring having a non-finitely generated projective module with finitely generated factor modulo its Jacobson radical.

7.3. Martin Doubek (MFF UK): OPERADIC COHOMOLOGY
In many cases, algebras of a given type (e.g. associative, Lie,...) can be descr ibed as representations of an operad. The category of operads is non-abelian category carrying a model structure. Derived functor H of a certain functor Der(-,End_V) from this category provides a nice cohomology theory for algebras representing the given operad. Thus resolutions (cofibrant replacements) of operads are of interest. We review several results on construction and significance of these resolutions. In particular, we explain how resolution in the abelian category of operadic mod ules can be used to find a first order approximation for H.

3.3. Pedro Guil (Universidad de Murcia): HEREDITARY RINGS WITH FINITELY GENERATED COTORSION ENVELOPE
Let R be a left hereditary ring. We show that the left cotorsion envelope of R is finitely generated if and only if R is a semiperfect cotorsion ring. Our proof is based on set-theoretical counting arguments. We also discuss some possible extensions of this result as well as its connection with other open questions. (Joint work with Dilek Pusat. Izmir Institute of Technology, Turkey.)

28.2. Sergio Estrada (Universidad de Murcia): MODEL STRUCTURES ON CQCO(X) AND RELATED QUESTIONS
Let Qco(X) be the category of quasi-coherent sheaves on a scheme X. We will overview the recent results from [1] concerning the interlacing between model structures and cotorsion pairs of complexes of quasi-coherent sheaves. We will also recall the equivalence between the category Qco(X) and a certain category of diagrams of modules. Then we will consider the problem of finding nice generators of Qco(X): the existence of locally free, flat, and locally flat Mittag-Leffler generators of Qco(X).
[1] S.Estrada, P.Guil Asensio, M.Prest, J.Trlifaj: Model category structures arising from Drinfeld vector bundles, arXiv: 0906.5213v1.

2010

20.12. Christmas party

29.11. Daniel Herden (Univ. Duisburg-Essen): PRESCRIBING ENDOMORPHISM RINGS OF ALEPH_N-FREE GROUPS 2

22.11. Daniel Herden (Univ. Duisburg-Essen): PRESCRIBING ENDOMORPHISM RINGS OF ALEPH_N-FREE GROUPS 1
We want to investigate in ZFC the problem of constructing arbitrarily large aleph_n-free groups G (for a fixed natural number n) with End G = Z. Recall that G is aleph_n-free if every subgroup of size < aleph_n is free. By now it is folklore to construct such groups using additional set-theoretic axioms, most notably Jensen's diamond principle. If we insist on proving this result in ordinary ZFC, then the known arguments fail: Both Corner's method of adding algebraically independent elements and Shelah's Black Box provide for groups, which are at most aleph_1-free but always fail to be aleph_2-free. To overcome this obstacle we will present groundbreaking new combinatorial tools ready for application to a wide range of problems about aleph_n-free (n< omega) structures to be attacked and solved in the future. (Joint work with Ruediger Goebel and Saharon Shelah.)

15.11. Iva Špakulová (Univ. Muenster): RESIDUAL FINITENESS OF ONE-RELATOR GROUPS
We have proved that with probability tending to 1, a one-relator group with at least 3 generators and the relator of length n is residually finite, virtually residually (finite p)-group for all sufficiently large p, and coherent. In this talk I will describe generic models on one-relator groups, properties related to residual finiteness and known results also in the the case of one-relator groups with two generators. I will present tools used in the proof, coming from both combinatorial group theory and theory of Random Walks and Brownian motions. (Joint work with Mark Sapir.)

1.11. Pierre Gillibert (MFF, ECC): CRITICAL POINT BETWEEN VARIETIES OF ALGEBRAS

25.10. Jan Šaroch (MFF): THERE ARE MANY NONEUCLIDEAN PID’S IN Q[x]

18.10. Katrin Leistner (Univ. Duisburg-Essen): INFINITARY EQUIVALENCE OF ABELIAN GROUPS AND MODULES

14.10. Brian A. Davey (La Trobe University, Australia): COUNTING THE RELATIONS COMPATIBLE WITH AN ALGEBRA

11.10. Jan Trlifaj (MFF): TILTING FOR COMMUTATIVE NOETHERIAN RINGS

4.10. Ruediger Goebel (Univ. Duisburg-Essen): CELLULAR COVERS FOR R-MODULES AND VARIETIES OF GROUPS

23.9. Lutz Struengmann (Univ. Duisburg-Essen): ON UNIVERSAL GROUPS AND PROBLEMS BY BAER AND KULIKOV

27.5. Otto Kerner (Math.Inst., Heinrich Heine Univ. Duesseldorf): CLUSTER ALGEBRAS OF RANK 3

25.5. Jan Stovicek (ECC-MFF): ROSICKY'S CONJECTURE FAILS FOR THE KRONECKER ALGEBRA

24.5. Otto Kerner (Math.Inst., Heinrich Heine Univ. Duesseldorf): THE UNIVERSAL PARAMETRIZING SPACE FOR WILD HEREDITARY ALGEBRAS

10.5. Jan Trlifaj (MFF): 2-TILTING FOR REGULAR LOCAL RINGS: DIVISIBILITY, LOCALIZATION, AND BEYOND

3.5. David Pospisil (MFF): CLASSIFICATION OF TILTING CLASSES FOR 2-DIMENSIONAL REGULAR RINGS

26.4. Pierre Gillibert (MFF): AN INFINITE COMBINATORIAL STATEMENT WITH A POSET PARAMETER

19.4. Libor Barto (MFF): THE COMPLEXITY OF LIST HOMOMORPHISM PROBLEMS

12.4. Jan Trlifaj (MFF): THE NEEMAN-ROSICKY PROBLEM FOR (LOCALLY) GROTHENDIECK CATEGORIES

22.3. Pavel Prihoda (MFF): CLUSTER ALGEBRAS II

15.3. David Pospisil (MFF): CLUSTER ALGEBRAS I

8.3. R.McKenzie (Vanderbilt Univ.): PARALLELOGRAM TERMS, FINITELY RELATED CLONES, SPARSE RELATIONAL CLONES

22.2. Jan Stovicek (ECC): COTORSION PAIRS IN EXACT CATEGORIES AND APPLICATIONS

4.1. Jan Saroch (MFF UK): ON A UNIVERSAL DEFINITION OF Z IN Q

2009

14.12. Christmas party

30.11. David Pospisil (MFF UK): TILTING MODULES OVER REGULAR DOMAINS

23.11. Jan Trlifaj (MFF UK): KAPLANSKY CLASSES

16.11. Jan Stovicek (MFF UK): FUNCTOR VALUED INVARIANTS OF KNOTS, LINKS AND TANGLES

2.11. Pierre Gillibert (Univ. Caen): CRITICAL POINTS BETWEEN VARIETIES OF LATTICES

26.10. Pavel Prihoda (MFF UK): GENERALIZED LATTICES OVER LATTICE-FINITE ORDERS

19.10. L. van den Dries (Univ. Illinois): LOGARITHMIC - EXPONENTIAL SERIES

12.10. L. van den Dries (Univ. Illinois): MODEL THEORY OF REALS AND O-MINIMALITY

8.6. P. Růžička (MFF UK): THE BANACHEWSKI FUNCTION AND V(R) OF COUNTABLE VON NEUMANN REGULAR RINGS

26.5. Cora Stack (Inst. of Technology, Dublin): STRUCTURE OF NILPOTENT ALGEBRAS

22.5. Jindrich Zapletal (University of Florida / MU AVCR): SYSTEMATIZATION OF BOREL EQUIVALENCES AND DYNAMIC PROPERTIES OF GROUPS

21.5. Vojtěch Rödl (Emory University, USA): THE REGULARITY LEMMA AND ITS APPLICATIONS

11.5. Peter Mayr (Univ. Linz): ARE POLYNOMIAL CLONES OF MAL'CEV ALGEBRAS FINITELY RELATED?

27.4. Jan Trlifaj (MFF UK): MODULES DETERMINED BY THEIR ANNIHILATOR CLASSES

20.4. Jan Žemlička (MFF UK): NO LOOPS CONJECTURE

16.4. Tobias Kenney (Cambridge/UMB Banska Bystrica): GRAPHICAL ALGEBRAS (A NEW APPROACH TO CONGRUENCE LATTICES)

6.4. Jan Šťovíček (NUST Trondheim & MFF UK): SIGMA-COTORSION MODULES AND FIRST ORDER THEORIES VIA DERIVED CATEGORIES

23.3. Jan Trlifaj (MFF UK): ALMOST FREE MODULES VIA TENSOR PRODUCTS

16.3. J.Kortelainen (Univ. Oulu): ON THE STRUCTURE OF COMMUTATIVE CONTEXT-FREE LANGUAGES

9.3. Jan Šťovíček (NUST Trondheim & MFF UK): RELATIVE HOMOLOGICAL ALGEBRA AND HOMOTOPY CATEGORIES OF COMPLEXES

2.3. M. Tamer Kosan (GIT): EXCELLENT EXTENSIONS OF RINGS

9.2. Dolors Herbera (UA Barcelona): BIG PROJECTIVE MODULES OVER NOETHERIAN SEMILOCAL RINGS

5.1. Jan Trlifaj (MFF UK): DRINFELD VECTOR BUNDLES

2008

22.12. Christmas party

15.12. Miroslav Korbelář (MFF UK): SUBDIRECTLY IRREDUCIBLE COMMUTATIVE RADICAL RINGS

8.12. Pawel Idziak (Univ. Krakow): DECIDABILITY OF FIRST AND SECOND ORDER THEORIES OF ALGEBRAS

1.12. P. Guil Asensio (Univ. Murcia): INDECOMPOSABLE OBJECTS IN COTORSION THEORIES

24.11. S. Estrada Dominguez (Univ. Almeria and Univ. Murcia): QUILLEN MONOIDAL MODEL STRUCTURES FOR NONUNITAL ALGEBRAS

10.11. David Pospisil (MFF UK): COMMUTATIVE GORENSTEIN RINGS

3.11. David Pospisil (MFF UK): IWANAGA-GORENSTEIN RINGS

27.10. Alberto Facchini (Univ. Padova): MONOGENY CLASS, EPIGENY CLASS, UPPER PART, LOWER PART

13.10. Libor Barto (MFF UK): CONGRUENCE DISTRIBUTIVITY HAS BOUNDED WIDTH

6.10. Jan Trlifaj (MFF UK): DRINFELD MODULES

29.9. Roman Nedela (Slovenska akad. vied / Univ. Mateje Bela): RECENT PROGRESS IN MAP ENUNUMERATION

24.9. Otto Kerner (Heinrich Heine Univ. Duesseldorf): EXACT STRUCTURES IN THE CATEGORIES OF REGULAR MODULES OVER WILD HEREDITARY ALGEBRAS

22.9. Jan Šťovíček (NUST Trondheim & MFF UK): EXT-ORTHOGONAL PAIRS FOR HEREDITARY RINGS

9.6. Marcin Kozik (ECC & Univ. Jagel. Krakow): COMMON LOOPS IN SOME CD GRAPHS

26.5. L.Angeleri Huegel (Univ. Varese): RECOLLEMENTS INDUCED BY TILTING MODULES

19.5. Pavel Příhoda (MFF): PROJECTIVE MODULES OVER SEMILOCAL NOETHERIAN RINGS 2

12.5. Petar Marković (Univ.Novi Sad): COMPLEXITY OF THE CSP

5.5. Miroslav Korbelář (MFF UK): SUBSEMIRINGS OF THE FIELD OF RATIONAL NUMBERS

21.4. Jan Trlifaj (MFF UK): APPROXIMATIONS OVER GORENSTEIN RINGS

14.4. David Pospíšil (MFF UK): AUSLANDER-BUCHWEITZOVY APROXIMACE

7.4. Jan Trlifaj (MFF UK): AECS OF FINITE CHARACTER

19.3. Jan Stovicek (NTNU Trondheim): TILTING ABELIAN CATEGORIES

17.3. Jan Trlifaj (MFF UK): SOCLE FINITENESS OF THE LOCAL COHOMOLOGY

3.3. Pavel Prihoda (MFF UK): MONOGENY DIMENSIONS OF MODULE HOMOMORPHISMS

25.2. J.D.Phillips (Wabash College, USA): A FEW HARD PROBLEMS FROM LOOP THEORY... BUT NOT FOR THE COMPUTER!

2007

10.12. Jan Trlifaj (MFF UK): ON HUNEKE'S CONJECTURE FOR LOCAL COHOMOLOGY

3.12. Jan Trlifaj (MFF UK): ABSTRACT ELEMENTARY CLASSES OF MODULES

26.11. Tamer Koşan (Gebze Inst. of Technology, Turkey): EXTENSIONS OF RINGS HAVING MCCOY CONDITION

20.11. Simion Breaz (Babes-Bolyai Univ., Cluj-Napoca): ABELIAN GROUPS WITH THE SAME ORTHOGONAL CLASSES

19.11. Ciprian Modoi (Babes-Bolyai Univ., Cluj-Napoca): CELLULAR APPROXIMATIONS IN ABELIAN CATEGORIES

12.11. Marcin Kozik (ECC a Jagelonska Univ. Krakow): IN THE DIRECTION OF THE CSP DICHOTOMY FOR TREES; THE SPECIAL TRIADS

29.10. Stelios Charalambides (NTNU Trondheim): UNIFORM MODULES RELATIVE TO A TORSION THEORY

22.10. Jan Trlifaj (MFF UK): ALMOST HEREDITARY RINGS (SOLUTION TO GREGORIO'S PROBLEM)

15.10. Miklos Maróti (University of Szeged): BOUNDED WIDTH ALGEBRAS IN CONGRUENCE DISTRIBUTIVE VARIETES

8.10. Aleš Drápal (MFF UK): NEW FOUNDATIONS FOR BASIC LOOP THEORY

1.10. Libor Barto (MFF UK): CONSTRAINT SATISFACTION PROBLEM: DICHOTOMY FOR SMOOTH DIGRAPHS

24.9. Otto Kerner (Heinrich Heine Univ. Duesseldorf): CLUSTER TILTED ALGEBRAS OF RANK 3

14.5. John Boxall (Universite de Caen): CLASS INVARIANT HOMOMORPHISMS FOR TORI AND ABELIAN VARIETIES

25.4. Andrei Marcus (Babes-Bolyai Univ., Cluj-Napoca): MORITA EQUIVALENCES INDUCED BY BIMODULES OVER HOPF-GALOIS EXTENSIONS

23.4. Pawel Idziak (Jagelonian Univ., Krakow): NUMERICAL INVARIANTS FOR VARIETES

23.4. Andrei Marcus (Babes-Bolyai Univ., Cluj-Napoca): EQUIVALENCES OF CATEGORIES IN MODULAR REPRESENTATION THEORY OF FINITE GROUPS

16.4. David Pospíšil (MFF UK): TILTING AND COTILTING MODULES OVER 1-GORENSTEIN RINGS

10.4. J. Šťovíček (NUST Trondheim & MFF UK): THE TELESCOPE CONJECTURE FOR ARTIN ALGEBRAS WITH VANISHING TRANSFINITE RADICAL

2.4. P. Příhoda (CRM IEC & MFF UK): PROJECTIVE MODULES OVER GENERALIZED WEYL ALGEBRAS

26.3. E.Chibrikov (Math.Inst., Novosibirsk): RIGHT-NORMED BASIS FOR FREE LIE ALGEBRAS AND LYNDON-SHIRSHOV WORDS

19.3. David Pospíšil (MFF UK): TILTING MODULES OVER COMMUTATIVE RINGS

5.3. Jan Trlifaj (MFF UK): MODULES OVER COMMUTATIVE GORENSTEIN RINGS

26.2. Jan Trlifaj (MFF UK): SEMI-BAER MODULES OVER GOLDIE RINGS

19.2. Libor Barto (MFF UK): BASKETS OF ESSENTIALLY ALGEBRAIC CATEGORIES

8.1. Marcin Kozik (ECC): COMPUTATIONAL COMPLEXITY IN UNIVERSAL ALGEBRA

2006

18.12. CHRISTMAS PARTY

4.12. Petr Somberg (MU, MFF UK): SYMMETRY ALGEBRAS OF (INVARIANT) DIFFERENTIAL OPERATORS

27.11. Jan Trlifaj (MFF UK): ABSTRACT ELEMENTARY CLASSES OF ROOTS OF EXT

20.11. Jan Žemlička (MFF UK): SELF-SMALL MODULES

13.11. Jan Šťovíček (NUST Trondheim & MFF UK): DEFINABILITY OF SIGMA-COTORSION MODULES

6.11. Miroslav Korbelář (MFF UK): EGGERT'S CONJECTURE

30.10. Marina Semenova (Mat. Inst., Univ. Novosibirsk): EMBEDDING LATTICES INTO CONVEXITY LATTICES OF TREE

23.10. Marina Semenova (Mat. Inst., Univ. Novosibirsk): EMBEDDING LATTICES INTO SUBSEMIGROUP LATTICES (A SURVEY)

16.10. Jan Šaroch: TELESCOPE CONJECTURE AND COTORSION PAIRS OF FINITE TYPE

9.10. Jan Trlifaj: RELATIVE BAER MODULES

8.9. Otto Kerner (Heinrich Heine Univ. Düsseldorf) CLUSTER TILTED ALGEBRAS OF RANK 3

15.5. Libor Barto: THE CATEGORY OF VARIETIES IS ALG-UNIVERSAL

24.4. G. Landsmann (RISC, Univ. Linz): D-MODULES AND THE WEYL ALGEBRA

10.4. Jan Šťovíček (NUST Trondheim & MFF UK): SIGMA-KOTORZNÍ MODULY A DEFINOVATELNOST

3.4. Lidia Angeleri Huegel (Univ. del'Insubria, Varese): A KEY MODULE OVER PURE-SEMISIMPLE HEREDITARY RINGS

31.3. P. Marković (Univ. Novi Sad): FINITE ALGEBRAS WITH FEW SUBPOWERS ARE TRACTABLE

27.3. Jiří Tůma: FINITE INTERVALS IN THE SUBGROUP LATTICES OF LOCALLY FINITE GROUPS

13.3. Pavel Růžička: FREE TREE AND WEHRUNG'S THEOREM

9.3. Rüdiger Göbel (Univ. Duisburg-Essen): ABSOLUTELY RIGID MODULES

27.2. Pavel Příhoda: BIG PROJECTIVE MODULES OVER SEMILOCAL NOETHERIAN RINGS

20.2. Jan Trlifaj: THE STRUCTURE OF STRONGLY FLAT MODULES OVER VALUATION DOMAINS

9.1. Jan Trlifaj: BAER MODULES

2.1. Jan Šťovíček (MFF UK Praha & NUST Trondheim): A GENERALIZATION OF THE KAPLANSKY THEOREM ON DECOMPOSITION OF PROJECTIVE MODULES

2005

19.12. CHRISTMAS PARTY

12.12. Jaroslav Ježek: SLIM GROUPOIDS

5.12. Pavel Růžička: 60 LET CLP

28.11. Pavel Příhoda: N-KOSOUVISLÉ ALGEBRY

21.11. Jan Trlifaj: HILLOVO LEMMA A JEHO DŮSLEDKY

14.11. Václav Flaška: ZS-POLOOKRUHY

7.11. Aleš Drápal: ALGEBRAICKÉ A GEOMETRICKÉ ASPEKTY LATINSKÝCH ZÁMĚN

24.10. Jan Šťovíček (MFF UK Praha & NUST Trondheim): KONEČNÝ TYP VYCHYLUJÍCÍCH TŘÍD

17.10. Jan Šaroch: ÚPLNOST KOTORZNÍCH PÁRŮ A TELESKOPICKÁ HYPOTÉZA

10.10. Jan Trlifaj: TRANSFER VYCHYLUJÍCÍCH TŘÍD

23.5. Pavel Příhoda: PROJECTIVE MODULES HAVING FINITELY GENERATED RADICALFAKTORMODUL

16.5. Vladimír Souček: LIE ALGEBRA HOMOLOGY AND MACDONALD-KAC FORMULAS

2.5. Otto Kerner (Heinrich-Heine Univ. Duesseldorf): REPRESENTATIONS OF WILD HEREDITARY ALGEBRAS

26.4. Wolfgang Windsteiger (Johannes-Kepler-Univ. Linz): A SYSTEM FOR MATHEMATICAL THEORY EXPLORATION

25.4. Septimiu Crivei (Babes-Bolyai Univ. Cluj): GRUSON-JENSEN DUALITY FOR IDEMPOTENT RINGS

19.4. Simion Breaz (Babes-Bolyai Univ. Cluj): SELF-SMALL ABELIAN GROUPS OF FINITE TORSION FREE RANK

18.4. Aleš Drápal: CC-LOOPS, CODES, AND THE MONSTER

11.4. C. Hollanti (Univ. Turku and Turku Centre for Comp. Sci): APPLICATIONS OF CYCLIC ALGEBRAS AND ORDERS IN SPACE-TIME CODING

4.4. Jan Trlifaj: ALL TILTING MODULES ARE OF COUNTABLE TYPE

22.3. Pierre Matet (Universite de Caen): HALES-JEWETT THEOREM

21.3. Petr Somberg: LIE ALGEBRA COHOMOLOGY

14.3. Bálint Felszeghy (Univ. of Techn. and Economy, Budapest): THE LEX GAME

7.3. Jan Trlifaj: COTILTING MODULES ARE PURE-INJECTIVE (IN ZFC)

28.2. Pavel Příhoda: MATLIS PROBLEM OVER HEREDITARY RINGS

10.1. Jan Šaroch: VYCHYLUJÍCÍ A KOVYCHYLUJÍCÍ MODULY A GÖDELŮV AXIOM KONSTRUOVATELNOSTI

2004

13.12. Tomáš Kepka: PROBLÉM Z TEORIE ČÍSEL

6.12. Petr Vojtěchovský: ROZŠÍŘENÍ ZALOŽENÁ NA STEINEROVÝCH TROJICÍCH

22.11. Jan Trlifaj: TIGHT SYSTEMS FOR MODULES OF PROJECTIVE DIMENSION 1

15.11. Jan Žemlička: IDEMPOTENTS IN STEADY RINGS

8.11. Pavel Příhoda: THE WEAK KRULL-SCHMIDT THEOREM FOR INFINITE DIRECT SUMS OF UNISERIAL MODULES

1.11. Pavel Růžička: APPLICATIONS OF UNIFORM REFINEMENT PROPERTIES SEMILATTICES

25.10. Jiří Tůma: ON SIMULTANEOUS REPRESENTATIONS OF DISTRIBUTIVE SEMILATTICES

18.10. Rüdiger Göbel (Univ. Duisburg-Essen): GROUPS HAVING A SIMPLE AUGMENTATION IDEAL IN THEIR GROUP RINGS

11.10. Jan Trlifaj: GAMMA-SEPARATED COVERS

4.10. Volkmar große Rebel (Univ. Dortmund): GENERALIZED TETRAHEDRON GROUPS AND THE TITS ALTERNATIVE

14.5. Franz Winkler (Techn. Univ. Linz): APPLICATION OF SYMBOLIC COMPUTATION TO ROBOTICS

11.5. Franz Winkler (Techn. Univ. Linz): APPLICATION OF SYMBOLIC COMPUTATION TO ROBOTICS

11.5. Franz Winkler (Techn. Univ. Linz): TOPICS IN GROEBNER BASES

10.5. Franz Winkler (Techn. Univ. Linz): ALGEBRAIC GEOMETRIC COMPUTATION

3.5. Jan Trlifaj: MATLISOVY LOKALIZACE

26.4. David Stanovský: LINEÁRNÍ TEORIE GRUPOIDŮ

16.4. Shmuel Zelikson (Universite de Caen): REPRESENTATION THEORY OF FINITE DIMENSIONAL LIE ALGEBRAS

15.4. Shmuel Zelikson (Universite de Caen): REPRESENTATION THEORY OF FINITE DIMENSIONAL LIE ALGEBRAS

5.4. Jaroslav Ježek: DEFINOVATELNOST PRO KOMUTATIVNÍ GRUPOIDY

29.3. Jan Trlifaj: MODULY NAD DĚDIČNÝMI KONEČNĚ-DIMENZIONÁLNÍMI ALGEBRAMI

22.3. Pavel Příhoda: SPOČETNÉ DIREKTNÍ SUMY UNISERIÁLNÍCH MODULŮ NAD (ZPRAVA) ŘETĚZCOVÝMI OKRUHY

15.3. Otto Kerner (Math. Inst., Heinrich-Heine-Universitaet Duesseldorf): GABRIEL'S THEOREM

2003

15.12. Christmas party

8.12. D. Donovan (Univ. Queensland): ON MINIMAL DEFINING SETS FOR STEINER TRIPLE SYSTEMS

1.12. Fred Wehrung (Univ. Caen): IDEAL LATTICES OF REGULAR RINGS WITH FINITE STABLE RANK

27.11. M. Ploscica (Math. Inst. SAS, Kosice): CONGRUENCE LATTICES OF ALGEBRAS IN CD-VARITIES

24.11. K. Rangaswami (Univ. Colorado): ON TORSION-FREE MODULES OF FINITE RANK OVER DISCRETE VALUATION DOMAINS

20.11. E. Blagoveshchenskaya (St. Petersburg): THE BAER-KAPLANSKY THEOREM AND ITS CONSEQUENCES FOR SOME ALMOST COMPLETELY DECOMPOSABLE GROUPS

10.11. Fred Wehrung (Univ. Caen): THE COMPLEXITY OF VON NEUMANN'S COORDINATIZATION

3.11. Fred Wehrung (Univ. Caen): SUBLATTICES OF BIALGEBRAIC LATTICES

20.10. V. Shcherbakov (Chisinau): ON N-ARY QUASIGROUPS AND SOME OF THEIR APPLICATIONS

13.10. Jan Trlifaj: TILTING AND COTILTING MODULES OF HOMOLOGICAL DIMENSION ONE

6.10. Pavel Prihoda: V(M) OF A SERIAL MODULE OF FINITE GOLDIE DIMENSION (A generalization of the Weak Krull-Schmidt Theorem)

23.5. Patrick Dehornoy (University of Caen, Francie): BRAID-BASED CRYPTOGRAPHICAL SCHEMES

22.5. Patrick Dehornoy (University of Caen, Francie): BRAID GROUPS AND BRAID ALGORITHMS

5.5. Slavnostní seminář u příležitosti 65. narozenin docenta Ladislava Berana

7.4. Jaroslav Ježek: O KVAZIIDENTITÁCH A PODOBNÝCH VĚCECH

3.3. P. P. Pálfy: ON THE ISOMORPHISM PROBLEM OF CAYLEY GRAPHS

24.2. Csaba Schneider (Univ. of Western Australia, Perth): PERMUTATION GROUPS AND CARTESIAN DECOMPOSITIONS

2002

18.11. Jaroslav Ježek

11.11. Tomáš Kepka: COMMUTATIVE RADICAL RINGS

4.11. Robert El Bashir: COREFLECTIONS AND THEIR GENERALIZATIONS

21.10. P.CSörgö (Budapest): SUPER SOLUBLE GROUPS

24.6. Kenneth Johnson (Pensylvania State University): GROUP REPRESENTATION THEORY BY THE HISTORICAL ROUTE

19.6. Friedrich Wehrung (Univ. Caen): SOLVING ALGEBRAIC PROBLEMS WITH BOOLEAN VALUED MODELS IV

18.6. Friedrich Wehrung (Univ. Caen): SOLVING ALGEBRAIC PROBLEMS WITH BOOLEAN VALUED MODELS III

13.6. John Boxall (Univ. Caen): ELLIPTIC CURVES IN CRYPTOGRAPHY II

12.6. John Boxall (Univ. Caen): ELLIPTIC CURVES IN CRYPTOGRAPHY I

12.6. Friedrich Wehrung (Univ. Caen): SOLVING ALGEBRAIC PROBLEMS WITH BOOLEAN VALUED MODELS II

11.6. Friedrich Wehrung (Univ. Caen): SOLVING ALGEBRAIC PROBLEMS WITH BOOLEAN VALUED MODELS I

13.5. P. Příhoda: ÚPLNÉ AFINNÍ POLOGRUPY

6.5. J.Trlifaj: STRUKTURA LIM P1 (ŘEŠENÍ FUCHSOVA PROBLÉMU 22)

29.4. W. Holubowski (Tech. Univ. Gliwice): FREE GROUPS OF INFINITE UNITRIANGULAR MATRICES

22.4. František Matúš (UTIA Praha): PODMÍNĚNÁ ZÁVISLOST V GAUSOVSKÝCH VEKTORECH A IDEÁLY POLYNOMŮ

15.4. Jiří Rosický (Masarykova Univerzita v Brně): KOTORZNÍ TEORIE A MODELOVÉ KATEGORIE

25.3. Oldřich Kowalski (MFF UK): O JEDNOM KOMBINATORICKÉM PROBLÉMU SPOJENÉM SE STUDIEM HOMOGENNÍCH GEODETIK NA LIEOVÝCH GRUPÁCH S INVARIANTNÍ METRIKOU

18.3. László Fuchs (Tulane University): TORSION-FREENESS FOR RINGS WITH ZERO DIVISORS

25.2. Lidia Angeleri Hügel (LMU, Mnichov): THE AUSLANDER-REITEN FORMULA

7.1. Štěpán Holub: LINEAR SIZE TEST SETS FOR CERTAIN COMMUTATIVE LANGUAGES

2001

17.12. Jan Trlifaj: APPROXIMATIONS AND INVERSE LIMITS

10.12. Thomas Kucera (Univ. of Manitoba): INJECTIVE ENVELOPES AND THE AXIOM OF CHOICE

3.12. Tomáš Kepka: KOMUTATIVNÍ RADIKÁLOVÉ OKRUHY

26.11. Fred Wehrung (Univ. Caen): DIMENSIONS OF MODULAR AND NON-MODULAR LATTICES

19.11. Jiří Velebil (FEL ČVUT): REFLECTIVE AND COREFLECTIVE SUBCATEGORIES OF PRESHEAVES

12.11. Marina Semenova (Matematicheskij Institut, Univ. Novosibirsk):    IRREDUNDANT DECOMPOSITIONS IN COPLETE LATTICES

29.10. Jan Žemlička:    CONSTRUCTIONS OF SEMIARTINIAN RINGS

22.10. Robert El Bashir:    COVERING MORPHISMS OF MODULES

11.10. Otto Kerner (Heinrich Heine Univ. Duesseldorf):    WILD HEREDITARY ALGEBRAS 2

8.10. Otto Kerner (Heinrich Heine Univ. Duesseldorf):    WILD HEREDITARY ALGEBRAS 1

4.10. David Bedford (Univ. of Keele, Great Britain):    DEFINING SETS FOR GROUPS BASED LATIN SQUARES

19.9. M.Dokuchaev (Univ. Sao Paolo):    PARTIAL ACTIONS OF GROUPS, PARTIAL GROUP RINGS AND CROSSED PRODUCTS

14.6. Miklos Maroti (Vanderbilt University):    THE VARIETY GENERATED BY TOURNAMENTS

4.6. Juha Kortelainen (University of Oulu):    ON FINITENESS CONDITIONS FOR SEMIGROUPS

21.5. Alexander Elashvili :    ABOUT INDEX OF FINITE DIMENSIONAL LIE ALGEBRAS

14.5. Jaroslav Ježek :    NOVĚJŠÍ VÝSLEDKY O VARIETĚ GENEROVANÉ TURNAJI

20.4. Patrick Dehornoy (Univ. Caen):    COMPLETE SEMIGROUP PRESENTATIONS

9.4. T.Kepka :    ROZŠÍŘENÍ KONEČNĚ GENEROVANÝCH KOMUTATIVNÍCH OKRUHŮ

2.4. V. Dlab (Carleton Univ., Ottawa):    STANDARDNĚ KOSZULOVY ALGEBRY

26.3. L.G.Kovacs (ANU, Canberra):    MODULE STRUCTURE OF FREE LIE ALGEBRAS

19.3. Jan Trlifaj :    VYCHYLUJÍCÍ MODULY A FINITISTICKÉ DIMENZE

12.3. Tomáš Kepka :    RADIKÁLOVÉ OKRUHY

5.3. Lidia Angeleri Hügel (LMU, Mnichov):    COVERS AND ENVELOPES VIA ENDOPROPERTIES

26.2. Jaroslav Ježek:    NĚKTERÉ KOMBINATORICKÉ STRUKTURY

2000

4.12. Aleš Drápal:    SÍLA ORBIT

27.11. Jan Žemlička:    UNISERIÁLNÍ MODULY NAD ŘETĚZOVÝMI OKRUHY

20.11. Jan Trlifaj:    THE FINITISTIC DIMENSION CONJECTURES

13.11. Pavel Růžička:    MAXIMAL SEMILATTICE QUOTIENTS OF DIMENSIONAL GROUPS

6.11. Jiří Tůma:    DIMENZNÍ GRUPY

30.10. Simone Wallutis: "The lattice of cotorsion theories is chaotic"

23.10. Robert El Bashir: "Čistoty a pokrytí"

16.10. Tomáš Kepka:

9.10. Jan Trlifaj: "Whitheadův problém v dimenzi 2"

29.5. "SLAVNOSTNÍ SEMINÁŘ U PŘÍLEŽITOSTI SEDMDESÁTÝCH NAROZENIN PROFESORA LADISLAVA PROCHÁZKY"

17.4. Jan Trlifaj: "KOTORZNÍ MODULY"

10.4. Ladislav Beran: "KREJČOVSKÉ DÍLO V TEORII SVAZŮ"

3.4. Alexander Elashvili: "A MAXIMAL COMMUTATIVE SUBALGEBRA OF THE MATRIX C-ALGEBRA"   

27.3. Alexander Elashvili:    A CLASSIFICATION OF TRIVECTORS OF 9-DIMENSIONAL C-SPACE, 2

20.3. Alexander Elashvili:    A CLASSIFICATION OF TRIVECTORS OF 9-DIMENSIONAL C-SPACE, 1

13.3. Tomáš Kepka:   KVAZIGRUPY DUÁLNÍCH ZLOMKŮ A KOREFLEXE

6.3. M. Hušek:   CHARAKTERIZACE MODULŮ, KTERÉ TVOŘÍ ÚPLNOU PODKATEGORII ABELOVSKÝCH GRUP

28.2. Tomáš Kepka:   HAMILTONOVSKÉ TRIMEDIÁLNÍ KVAZIGRUPY

1999

13.12. Robert El Bashir:   THE DENSITY OF PURE SUBMODULES

6.12. Jiří Tůma:   REPREZENTACE DISTRIBUTIVNÍCH POLOSVAZU IDEÁLY LOKÁLNĚ MATICOVÝCH ALGEBER

29.11. Jaroslav Ježek: VARIETA GENEROVANÁ USPOŘÁDANÝMI MNOŽINAMI

22.11. Fred Wehrung:  DIMENSION THEORY OF PARTIALLY ORDERED SYSTEMS WITH ORTHOGONALITY

  8.11. Tomáš Crhák: REALIZACE SIMPLICIÁLNÍCH MNOŽIN POMOCÍ LOKÁLNĚ KONVEXNÍCH ALGEBER

25.10. Enrico Vitale: LOCALIZATIONS: FROM PRESHEAVES TO VARIETIES

18.10. Tomáš Kepka: SOUBLINUV PROBLÉM A JEHO ŘEŠENÍ

11.10. Jan Trlifaj: PRECOVERS INDUCED BY EXT

4.10. Alexander Elashvili: A CLASSIFICATION OF THE PRINCIPAL NILPOTENT PAIRS IN SIMPLE LIE ALG.

27.9. Paul C. Eklof: THE STRUCTURE OF EXT (A, Z) WHEN HOM (A, Z) = 0

14.6. Ján Mináč:IS THE COHOMOLOGY OF GROUPS USEFUL IN DAILY LIFE?

26.5. Cristina Pedicchio: EXACTNESS CONDITIONS OF VARIETIES AND QUASIVARIETIES OF ALGEBRAS

17.5. Manfred Droste: HOMOGENEOUS STRUCTURES IN ALGEBRA AND COMPUTER SCIENCE

10.5. M. Hušek: PRODUCTIVITY OF COREDUCTIVE CLASSES OF TOPOLOGICAL GROUPS

3.5. Vlastimil Dlab: THE CONCEPT OF STRACIFICATION OF ALGEBRAS

26.4. Tomáš Kepka: FRACTIONS AND DUAL FRACTIONS

19. 4. Ladislav Bican: ALMOST PRECOVERS

12.4. Juha Kortelainen: ON TEST SETS AND WORLD EQUATIONS

29.3. Jan Trlifaj: LARGE INDECOMPOSABLE ROOTS OF EXT

22.3. Jiří Tůma: SIMULTÁNNÍ REPREZENTACE DISTRIBUTIVNÍCH SVAZU

8.3. Pavel Růžička:REALIZACE DISTRIBUTIVNÍCH SVAZŮ JAKO SVAZU IDEÁLU VON NEUMANNOVSKY

REGULÁRNÍCH OKRUHU

1.3. Lawrence Somer:PSEUDOPRIMES, PERFECT NUMBERS,AND A PROBLEM OF LEHMER

1998

25.05. Markus Schmidmeier: Knots, tensor product, and modules over quantum groups

18.05. Ladislav Bican: Ultraproducts of Butler groups

11.05. Jan Trlifaj: Tilting preenvelopes and cotilting precovers

04.05. Petr Vojtěchovský: On distances of cyclic groups

27.04. Štěpán Holub:Words, subwords and their powers

20.04. Alberto Tonolo (Univ. Padova): On complementarity of quasi-tilting triples

06.04. Aleš Drápal: Distances of 2-groups

30.03. Vlastimil Dlab (Carleton Univ., Ottawa): On stratifications of algebras

23.03. Jan Trlifaj: Cotilting and a hierarchy of almost cotorsion groups

16.03. Ladislav Beran: On covering in lattices

09.03. Tomáš Kepka: Simple non-commutative semirings

02.03. Robert El Bashir: Semirings of positive elements

23.02. Jaroslav Ježek: Minimal big lattices

05.01. Jaroslav Ježek: The variety generated by tournaments

1997
15.12. Aplikace (výjezdní seminář, v laboratoři KA)

8.12. L. Bican: Precovers

01.12. J. Krempa(Univ. Warsaw): Lattice approach to uniform dimension

24.11. O. Gorbačuk(Univ. Lviv): Spiliting torsion in categories of modules and differential closed fields

17.11. T. Kepka: Products of Abelian groups and radical rings

10.11. M. Schmidmeier: Artinian PI-rings witch are not artin algebras

03.11. L. Beran: Lattice Meanders

27.10. W. Zimmermann(LMU, Muenchen): Modules which acc for finite matrix subgroups

20.10. J. Trlifaj: Dimension sequences for semiartinian regular rings

13.10. L. Angeleri Huegel (LMU, Muenchen): On a preprojective module describing the underlying algebra

06.10. Tomáš Kepka: The Hoelder-Cartan-Hilbert-Chion-Tallini Theorm

23.06. William Lampe (University of Hawaii): Lattice Representations in General Algebra

19.05. A. Elashvili (Math. Inst. Georg. Acad.Sci.): A classification of zero-compact nilpotent elements in simple Lie Algebras

12.05. J. Žemlička: Steadiness in certain classes of rings

05.05. J. Trlifaj: Cofinal decreasing chains in modules

28.04.  A.  Elashvili (Math. Inst. Georg. Acad. Sci.): Hermite receprocity for regular representations of cyclic group