Organized by Arturo Espinosa Baro, Alexis Marchand, and Piotr Nowak
Fridays, 10:45 -- 12:00 (60 min talk + 15 min questions), room 106 at IM PAN
Upcoming talks
30/10/2026, 10:45--12:00
Speaker: Aleksander Skenderi (Uniwersytet Jagielloński)
Title: Discrete subgroups of Lie groups and their critical exponents
Abstract: An important quantity in the study of discrete groups of isometries of Riemannian manifolds, Gromov hyperbolic spaces, and other interesting geometric objects is the critical exponent. For a discrete subgroup of isometries of the quaternionic hyperbolic space or octonionic projective plane, Kevin Corlette established in 1990 that the critical exponent detects whether a discrete subgroup is a lattice or has infinite covolume. Precisely, either the critical exponent equals the volume entropy, in which case the discrete subgroup is a lattice, or the critical exponent is less than the volume entropy by some definite amount, in which case the discrete subgroup has infinite covolume. In 2003, Leuzinger extended this gap theorem for the critical exponent to any discrete subgroup of a Lie group having Kazhdan's property (T) (for instance, a discrete subgroup of SL(n,R), where n is at least 3).
In this talk, I will present a result which shows that no such gap phenomenon holds for discrete semigroups of Lie groups. More precisely, given any Zariski dense discrete subgroup of a Lie group, it contains free, finitely generated, Zariski dense subsemigroups whose critical exponents are arbitrarily close to that of the ambient discrete subgroup. As an application of this, the critical exponent is lower semicontinuous in the Chabauty topology. We will also discuss some applications of this lower semicontinuity result to the study of locally symmetric spaces.
Time permitting, I will discuss recent work generalizing the classical Borel Density Theorem to the setting of infinite covolume discrete subgroups of sufficiently large critical exponent.
All concepts will be explained from scratch, and we will focus on the case of matrix groups to make the presentation more concrete. No AI was used in any form for the mathematics presented in this talk; the speaker prefers to preserve the familiar traditions and manner of doing mathematics.
06/11/2026, 10:45--12:00
Speaker: Alexis Marchand (IM PAN)
Title: The Hausdorff property for bounded cohomology via ultraproducts
Abstract: (Joint work with Piotr Nowak.) Bounded cohomology is a functional-analytic variant of group cohomology. Despite its many connections with geometry and topology, it can be a mysterious object. This talk will be about the property of bounded cohomology being Hausdorff. We will explain how this property can be read in asymptotic cohomology, yet another cohomology theory that was introduced recently to study stability properties of groups. This makes use of ultraproduct techniques invented by Bader and Sauer in the context of property (T), and that we will explain.
13/11/2026, 10:45--12:00
Speaker: Pratyush Mishra (Rényi Alfréd Matematikai Kutatóintézet)
Title: TBA
Abstract: TBA
20/11/2026, 10:45--12:00
Speaker: Monika (Uniwersytet Warszawski)
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27/11/2026, 10:45--12:00
Speaker: Martina Conte (Universität Bielefeld)
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04/12/2026, 10:45--12:00
Speaker: Nima Hoda (Uniwersytet Wrocławski)
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11/12/2026, 10:45--12:00
Speaker: Ismael Sierra (University of Glasgow)
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18/12/2026, 10:45--12:00
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08/01/2026, 10:45--12:00
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15/01/2026, 10:45--12:00
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22/01/2026, 10:45--12:00
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Previous talks
23/10/2026, 10:45--12:00
Speaker: Arturo Espinosa Baro (IM PAN)
Title: Open covers of aspherical spaces satisfying $\pi_1$-constraints and bounded Adamson cohomology.
Abstract: Given a topological space X and a family of subgroups F of the fundamental group of X, the F-category of X is given as one less than the cardinality of the smallest cover of X by open subsets whose fundamental groups lie in F. One particular case of interest is when F is taken as the family of amenable subgroups, in which case the F-category is known as the amenable category of X, and whose (non-)maximality has interesting connections with Gromov's simplicial volume. We study F-categories of aspherical spaces and obtain cohomological lower bounds, a maximality result and bounded cohomology classes whose vanishing properties are crucial for determining F-categories. For this purpose, we study the bounded Adamson cohomology of a family of subgroups and discuss universality properties of bounded cohomology classes. We apply our techniques to derive some applications to the study of the monotonicity of F-categories under degree-one maps between manifolds and to answer in the negative a question of P. Capovilla, C. Löh and M. Moraschini on whether or not the amenable category of closed connected oriented aspherical manifolds equals the maximal dimension for which their comparison map in bounded cohomology with real coefficients is non-trivial. This talk is based on joint work with Stephan Mescher.
09/10/2026, 10:45--12:00
Speaker: Prem Nigam Kar (IM PAN)
Title: Linear Constraint System Games and the Non-Hyperlinear Group Problem
Abstract: Linear Constraint System (LCS) games arose in quantum information theory as a generalization of the Mermin-Peres magic square game, which can be used to give an alternative proof of the celebrated Bell’s theorem in quantum mechanics. One can associate a solution group to each LCS game, which encodes its “quantum strategies.” Solution groups and LCS games have played a key role in a number of important results in quantum information theory over the past decade, most notably in the negative resolution of the strong and middle Tsirelson problems by William Slofstra. However, the weak Tsirelson problem, which was solved for general nonlocal games, still remains open for LCS games. In this talk, after a quick introduction to quantum information theory, LCS games, and solution groups, we shall see how the weak Tsirelson problem for LCS games relates to the non-hyperlinear group problem and how the non-hyperlinear group problem itself relates to the non-sofic group problem, which was recently “resolved” by AI. The only prerequisite for this talk will be a basic understanding of bounded operators on Hilbert spaces.
02/10/2026, 10:45--12:00
Speaker: Diptesh Saha (IM PAN)
Title: An introduction to noncommutative ergodic theorems
Abstract: Noncommutative spaces can be viewed as generalisations of classical measure spaces. Birkhoff’s pointwise ergodic theorem is one of the most prominent results in classical analysis. In this talk, we will discuss various generalisations of this classical theorem to general group actions, and then explore some of their noncommutative analogues. We will highlight some of the key techniques involved and draw parallels between the classical and noncommutative settings. A basic understanding of classical measure theory will be assumed, and I will introduce and explain the relevant noncommutative counterparts as needed.
26/06/2026, 14:30 -- 15:30
Speaker: Jakub Szymański (Uniwersytet Warszawski)
Title: Uniform Kazhdan's Property (T)
Abstract: Proving that a specific group has Kazhdan's property (T) requires choosing a generating set and ensuring that the corresponding Kazhdan constant is strictly positive. The uniform property (T) is a strong generalization of this concept, where the infimum of Kazhdan constants with respect to all possible generating sets is a positive number. In my talk, I will present examples of Kazhdan groups both with and without the uniform property (T) and discuss some open cases.
29/05/2026, 14:30 -- 15:30
Speaker: Yash Lodha (Purdue University)
Title: A solution to the Wiegold problem on perfect groups
Abstract: A fundamental notion in group theory is the notion of the normal rank of a group. This is the smallest size of a set of elements, which if included in the set of relations, render the group trivial. The smallest size of the generating set of the group abelianization provides a natural lower bound for the normal rank. The 1976 Wiegold problem on perfect groups asks whether there exist finitely generated perfect groups whose normal rank is greater than one. We demonstrate that free products of finitely generated perfect left orderable groups have normal rank greater than one. This solves the Wiegold problem, since there are a plethora of such examples. This is joint work with Lvzhou Chen.
24/04/2026, 14:30 -- 15:30
Speaker: Joeri De Ro (IM PAN)
Title: Introduction to compact and discrete quantum groups
Abstract: Discrete quantum groups generalize classical discrete groups while exhibiting genuinely new (quantum) phenomena (e.g. non-unimodularity). In this introductory talk, we explain how the structure of a discrete quantum group can be recovered from the representation theory of its dual compact quantum group. We highlight the key ideas through examples and discuss how this perspective parallels classical harmonic analysis. No prior knowledge of quantum groups will be assumed.
17/04/2026, 14:30 -- 15:30
Speaker: Michal Ferov (University of South Bohemia)
Title: Willis' scale function for TDLC groups acting on trees with Tits' independence property P
Abstract: A group $G$ acting faithfully on a graph $X$ can be equipped with a permutation topology, making a totally disconnected topological group. If $G$ has finite suborbits then it is locally compact. Some properties of totally disconnected locally (TDLC) compact groups are captured by the Willis' scale function. We show that for TDLC groups acting on trees with Tits independence property P, the scale function can be computed from finite combinatorial data and and, as an application, we show that every uniscalar P-closed group is either horocyclic or compact-by-discrete.
14 to 16/04/2026 (detailed schedule below), minicourse
Speaker: Michal Ferov (University of South Bohemia)
Title: Gentle introduction to totally disconnected groups acting on trees
Abstract: The study of totally disconnected locally compact groups is an active area of research in modern mathematics, bringing together seemingly unrelated fields such as topology, descriptive set theory, functional analysis, representation theory, combinatorial and geometric group theory, and many more. In this minicourse I will give a brief introduction to the theory of totally disconnected locally compact groups and discuss some aspects of their actions on combinatorial structures, especially trees. Basic understanding of topology and group theory (on undergraduate level) will be assumed, nothing more.
Locations and times:
14/04/2026: 14:30 -- 15:30 -- Room 403
15/04/2026: 11:00 -- 12:00 -- Room 405
16/04/2026: 14:30 -- 15:30 -- Room 403
10/04/2026, 14:30 -- 15:30
Speaker: Sam Hughes (Universität Bonn)
Title: Quasihomomorphisms to real algebraic groups
Abstract: A quasihomomorphism is a map that satisfies the homomorphism relation up to bounded error. Fujiwara and Kapovich proved a rigidity result for quasihomomorphisms taking values in discrete groups, showing that all quasihomomorphisms can be built from homomorphisms and sections of bounded central extensions. We study quasihomomorphisms with values in real linear algebraic groups, and prove an analogous rigidity theorem. Based on joint work with Sami Douba, Francesco Fournier Facio, and Simon Machado.
08/04/2026, 11:00 -- 12:00, Room 403
Speaker: Julian Wykowski (University of Cambridge)
Title: Profinite Rigidity, Noetherian Domains, and Solvable Groups
Abstract: The question of profinite rigidity asks whether the isomorphism type of a group Γ can be recovered entirely from its finite quotients. In this talk, I will introduce the study of profinite rigidity in a different setting: the category of modules over a Noetherian domain Λ. I will explore properties of Λ-modules that can be detected via finite quotients and present two profinite rigidity theorems: one for free Λ-modules under a weak homological assumption on Λ, and another for all Λ-modules in the case when Λ is a Dedekind domain. Returning to groups, I will explain how these algebraic results yield new answers to profinite rigidity for several infinite classes of solvable groups that are of interest in combinatorial and geometric group theory. Time permitting, I will conclude with a sketch of future directions and ongoing collaborations that push these ideas further.
20/03/2026, 14:30 -- 15:30
Speaker: Antonio López Neumann (Université Paris Cité)
Title: Quantitative polynomial cohomology and applications
Abstract: Polynomial cohomology of groups was first introduced by Connes and Moscovici, and can be thought as a way of interpolating between bounded cohomology and usual group cohomology. Following work by Bader and Sauer, we introduce a quantitative version of polynomial cohomology and show that it coincides with group cohomology under polynomiality assumptions on filling functions. We give two applications of this result.
- We show that Betti numbers give an obstruction to L^p-measure equivalence of nilpotent groups for large values of p.
- We show vanishing of some cohomology spaces for non-uniform lattices in rank 1 simple Lie groups. In particular, we show that lattices acting on the octonionic hyperbolic plane enjoy a higher version of Kazhdan's property T.
This is based on joint work with Juan Paucar.
06/03/2026, 14:30 -- 15:30
Speaker: Bin Sun (Michigan State University)
Title: L2-Betti numbers of Dehn filling
Abstract: I will talk about joint work with Nansen Petrosyan about L2-Betti numbers of groups. Although L2-Betti numbers in general don’t interact well with taking quotients of groups, we prove that, for virtually compact special hyperbolic groups, group-theoretic Dehn filling preserves L2-Betti numbers.
27/02/2026, 14:30 -- 15:30
Speaker: Piotr Nowak (IM PAN)
Title: TBC
Abstract: TBC
13/02/2026, 10:45 -- 12:00
Speaker: Nicolas Vaskou (Université de Genève)
Title: Artin groups and the isomorphism problem
Abstract: Artin groups form a large class of infinite groups. They contain groups such as free abelian groups, free groups, braid groups, and many others. Despite an increasing interest in the topic, these groups remain quite mysterious in general, in the sense that many classical questions in geometric group theory are still unanswered for them. The first half of the talk will serve as an introduction to Artin groups and some standard tools in the theory. In the second half, I will talk specifically about the isomophism problem, and I will present a solution for certains families of Artin groups.
Minicourse: 10/02/2026 at 16:00, 11/02 at 16:00, and 12/02 at 14:30, in Room 403
Speaker: Mark Pengitore (IM PAN)
Title: Linearity criteria of automorphism groups of hyperbolic groups
Abstract: In this minicourse, we give criteria for linearity of automorphism groups of nonelementary hyperbolic groups using quantitative residual finiteness. In particular, we will demonstrate if you can detect elements of the hyperbolic group using characteristic epimorphisms to finite products of finite simple groups of Lie type whose size is at most a polynomial in word length, then the the automorphism group of the hyperbolic group admits a faithful finite dimensional representation over a field of characteristic 0. The main tools that are used are ultraproducts, a generalization of least common multiples to the setting of hyperbolic groups, and properties of finite simple groups of Lie type and their automorphism groups.
06/02/2026, 14:30 -- 15:30 [Note the unusual time]
Speaker: Will Cohen (University of Cambridge)
Title : Improving acylindrical actions on trees
Abstract:: Loosely speaking, an action of a group on a tree is acylindrical if long enough paths must have small stabilisers. Groups admitting such actions form a natural subclass of acylindrically hyperbolic groups, and an interesting feature of acylindrical actions on trees is that many properties of groups are inherited from their vertex stabilisers. In order to make use of this, it is important to have some degree of control over these stabilisers. For example, can we ask for these stabilisers to be finitely generated?
In this talk, I will introduce acylindrical actions and some stronger and related concepts, and discuss a method known as the Dunwoody—Sageev resolution that we can use to move between these concepts and provide positive answers to the above question in some cases.
19/12/2025, 10:45 -- 12:00
Speaker: Michał Marcinkowski (Uniwersytet Wrocławski)
Title: Sampling from finite groups
Abstract: We describe a simple method (a variant of the product replacement algorithm) that can be used to sample an element almost uniformly from a finite group. Using techniques developed by Kaluba, Nowak, and Kielak in their work on property (T) for Aut(F_n), we obtain the currently best estimates for the efficiency of this sampling procedure. This is joint work with Piotr Mizerka.
12/12/2025, 10:45 -- 12:00
Speaker: Mark Pengitore (IM PAN)
Title: A linearity criterion of automorphism groups of hyperbolic groups
Abstract: In this talk, we can give a general criterion for the automorphism group of nonelementary hyperbolic groups to be linear in terms of certain epimorphisms from the hyperbolic group to finite products of finite simple groups of Lie type. Potential applications include the question of nonlinearity of mapping class groups.
31/10/2025, 10:45 -- 12:00
Speaker: Arman Darbinyan (University of Southampton)
Title: Controlling Residual Finiteness: Growth, Computability, and Beyond
Abstract: In this talk, I will discuss a class of residually finite groups that provides strong control over various properties, including residual finiteness growth and its computability aspects. In particular, we will see how this class fully describes the spectra of sufficiently large residual finiteness growth functions up to the standard equivalence. I will also mention some corollaries concerning the word and conjugacy problems.
31/10/2025, 14:30 -- 15:30
Speaker: Conan Gillis (Cornell University)
Title: The Conjugator Length Function of the Baumslag-Gersten group.
Abstract: The Baumslag-Gersten group $G=\langle s_0, t \mid ts_0t^{-1} s_0(ts_0t^{-1})^{-1}=s_0^2 \rangle$, is a well-known example in geometric group theory, particularly for its non-elementary-recursive (non-E.R.) Dehn function. The best known algorithm for the conjugacy problem in $G$ has non-E.R. time complexity, and it is conjectured that no E.R. time algorithm exists. We study the conjugator length function $CL(n)$ of $G$, which provides another measure of complexity of the conjugacy problem based on $G$'s intrinsic geometry. First, we show that, for any $\epsilon>0$, $CL(n)$ is greater than $2^{2^{\cdots^2}}$ (up to a standard equivalence) where the power tower is of height $ \lfloor (1-\epsilon)\log n\rfloor$. In particular, this bound suggests that the conjugacy problem is not decidable in E.R. time. If time allows, we will further discuss a corresponding upper bound: $CL(n)$ is at most a power tower of height precisely $\lfloor \log n\rfloor$.
24/10/2025, 10:45 -- 12:00
Speaker: Sam Mellick (Jagiellonian University)
Title: Hutchcroft-Pete Redux
Abstract: Recently, Hutchcroft and Pete answered a longstanding question of Gaboriau by constructing cost one actions for infinite groups with Property (T). In this talk, I will present an alternative proof of this fact which also generalises to the locally compact setting.
The proof works via a natural notion of "Kazhdan optimal colourings". I will explain these, as well as the probabilistic interpretation on cost. No knowledge of probability theory will be assumed.
Joint work with Lukasz Grabowski and Hector Jardon-Sanchez.
17/10/2025, 10:45 -- 12:00
Speaker: Oli Jones (TU Berlin / Heriot-Watt University)
Title: Cyclic splittings of Artin groups
Abstract: Artin groups are a family of groups generalising right-angled Artin groups and braid groups; despite much study of specific subclasses, many questions about all Artin groups remain mysterious. In this talk I will present a complete characterisation of which Artin groups split (as an amalgamated product or HNN extension) over infinite cyclic subgroups. I will then discuss an application to the isomorphism problem for Artin groups, via a kind of maximal splitting called a JSJ decomposition. This talk is based on joint work with Giorgio Mangioni and Giovanni Sartori.
10/10/2025, 11:00--12:00
Speaker: Arturo Espinosa Baro (IM PAN)
Title: Homotopy invariants of LS-category type for aspherical spaces
Abstract: Since the introduction of LS-category in 1934 to give lower estimates on the number of critical points of smooth functions on manifolds, many different homotopy invariants inspired by LS-cat have been defined and studied. Amongst the most significant are the F-categories (especially the amenable category), the sectional category of Schwarz, and the different variants of topological complexities à la Farber. In this talk we will give a very short introduction to some of those invariants, focusing mostly on how they behave for K(G,1)-spaces, and we will present some recent developments on the field.
03/10/2025, 11:00 -- 12:00
Speaker: Dimitris Gerontogiannis (IM PAN)
Title: Spanier-Whitehead duality and Temperley-Lieb quantum symmetries
Abstract: The notion of Spanier-Whitehead duality can be generalised to the noncommutative setting of C*-algebras and KK-theory, where it is called KK-duality. As C*-algebras are noncommutative topological spaces in view of the Gelfand duality, C*-algebras with KK-duals can be thought of as noncommutative finite CW complexes. Therefore, a main utility of KK-duality is that it makes it possible to study C*-algebras by more classical methods. Interestingly, several C*-algebras associated with dynamical systems appear to have KK-duals. This talk is about the KK-duality of Cuntz-Pimsner algebras associated to Temperley-Lieb subproduct systems, a class of C*-algebras with rich quantum group symmetries and relations to topological Markov chains. This is joint work with Francesca Arici (Leiden) and Sergey Neshveyev (Oslo).
26/09/2025, 11:00 -- 12:00
Speaker: Alexis Marchand (IM PAN)
Title: Sharp spectral gaps for scl from negative curvature
Abstract: Stable commutator length is a measure of homological complexity of group elements, with connections to many topics in geometric topology, including quasimorphisms, bounded cohomology, and simplicial volume. The goal of this talk is to shed light on some of its relations with negative curvature. We will present a new geometric proof of a theorem of Heuer on sharp lower bounds for scl in right-angled Artin groups. Our proof relates letter-quasimorphisms (which are analogues of real-valued quasimorphisms with image in free groups) to negatively curved angle structures for surfaces estimating scl.
21/03/2025, 11:00 -- 12:00
Speaker: Jakub Szymański (University of Warsaw)
Title: Expansion of Integer Matrices over Various Rings
Abstract: Given a finite CW complex whose fundamental group has property (T), we can construct a family of cosystolic expanders over $\mathbb{R}$ through finite covers. However, the real challenge lies in obtaining expanders over $\mathbb{F}_2$. Therefore, the goal would be to adapt the proof to work with different rings in this context. In my talk, I will present conditions under which the expansion of morphisms defined by integer-valued matrices can be bounded over integers and finite fields, building on the work of Uri Bader and Roman Sauer.
07/02/2025, 11:00 -- 12:00
Speaker: Tattwamasi Amrutam (IM PAN)
Title: A Continuous Version of the Intermediate Factor Theorem
Abstract: Let $G$ be a discrete group. A $G$-space $X$ is called a $G$-boundary if the action of $G$ on $X$ is minimal and strongly proximal. In this talk, we shall prove a continuous version of the well-studied Intermediate Factor Theorem in the context of measurable dynamics. When a product group $G = \Gamma_1 \times \Gamma_2$ acts (by a product action) on the product of corresponding $\Gamma_i$-boundaries $\partial\Gamma_i$, we show that every intermediate factor
$X \times (\partial\Gamma_1 \times \partial\Gamma_2) \to Y \to X$
is a product (under some additional assumptions on $X$). We shall also compare it to its measurable analog proved by Bader-Shalom. This is a recent joint work with Yongle Jiang.
31/01/2025, 11:00 -- 12:00
Speaker: Mark Pengitore (IM PAN)
Title: Growth Functions and linearity of automorphism groups of hyperbolic groups
Abstract: This talk will introduce various growth functions associated to a finitely generated group which measure the difficulty of separating an element from the identity using epimorphisms to a fixed family of nonabelian finite simple groups with characteristic kernels as a function of the word length. As an application of these functions, we provide a characterization of when the automorphism group of a hyperbolic group is linear.
06/12/2024, 11:00 -- 12:00
Speaker: Jacopo Bassi (IM PAN)
Title: On regularity of boundary representations
Abstract: Biexactness and the (AO)-property can be considered as analytic counterparts of hyperbolicity for discrete groups. Motivated by the problem of determining whether they are equivalent, I will discuss an approach to the study of regularity properties of boundary actions/representations based on measurable dynamics. This approach will be used to study SL(3,Z) and to answer a question posed by C. Anantharaman-Delaroche.
22/11/2024, 11:00 -- 12:00
Speaker: Piotr Nowak (IM PAN)
Title: L2 Betti numbers and the coarse Baum-Connes conjecture
Abstract: I will explain how spectral gaps for cohomological Laplacians in higher degrees lead to obstructions to surjectivity of the coarse assembly map. This is joint work with Kang Li and Sanaz Pooya.
15/11/2024, 11:00 -- 12:00
Speaker: Antonio López Neumann (IM PAN)
Title: On growth of cocycles of isometric representations on L^p-spaces
Abstract: Cocycles of unitary representations appear naturally when dealing with analytic properties of groups, such as Property (T) or the Haagerup property. This talk is devoted to the study of their Banach analogues (often on L^p-spaces) and their asymptotic behaviour. Two natural questions arise.
- What information about the group do these asymptotics carry?
- Are there any differences when changing Hilbert coefficients by Banach coefficients?
The main technique we want to advertise is the use of random walk averages to obtain estimates on the diameter growth and the equivariant compression of cocycles.
08/11/2024, 11:00 -- 12:00
Speaker: Mark Pengitore (IM PAN)
Title: Automorphism groups of solvable groups of finite abelian ranks
Abstract: I will introduce the collection of solvable groups of finite abelian ranks, which is a group of solvable groups that have resisted many geometric techniques that are typically used in group theory. We will discuss basic examples, properties, and invariants of these groups. We will then introduce the Q-algebraic hull of a solvable group G of finite abelian ranks, which is a linear algebraic group that can be used to model automorphisms of G. As an application of this Q-algebraic hull, we finish by demonstrating that the outer automorphism group of a linear solvable group of finite abelian ranks is S-arithmetic when the Fitting subgroup is S-arithmetic, which is a generalization of a celebrated result of Baues-Grunewald.