Analytic and Geometric Group Theory At IMPAN

Organized by Mark Pengitore, Antonio López Neumann, and Piotr Nowak

Fridays at 11:00 - 12:30 at Room 106

Next Seminar

06/12/2024, 11:00 -- 12:30

Speaker: Jacopo Bassi (IM PAN)

Title: TBA

Abstract: TBA

Previous talks

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.