Organized by Mark Pengitore, Alexis Marchand, and Piotr Nowak
Fridays at 11:00 - 12:30 at Room 106
Next Seminar
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).
Upcoming talks
17/10/2025, 11:00 -- 12:00
Speaker: Oli Jones (TU Berlin / Heriot-Watt University)
Title: TBC
Abstract: TBC
31/10/2025, 11:00 -- 12:00
Speaker: Arman Darbinyan (University of Southampton)
Title: TBC
Abstract: TBC
31/10/2025, 14:30 -- 15:30
Speaker: Conan Gillis (Cornell University)
Title: TBC
Abstract: TBC
Previous talks
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.