November 24:

• Apurva Seth (University of Oxford, UK)

• Sergio Girón Pacheco (KU Leuven, Belgium)

November 17:

• Sanaz Pooya (University of Potsdam, Germany)

• Ben Bouwen (Université Paris Cité, France)

November 10:

• Kai Toyosawa (University of Muenster, Germany)

• Rémi Barritault (Université Paris Cité, France)

November 3:

• Ferdinand Jacobé de Naurois (University of Oxford, UK)

• Kostyantyn Krutoy (Université Paris Cité, France)

October 20:

• Manish Kumar (KU Leuven, Belgium)
  
  Title: Coarse rigidity in von Neumann algebras via derivations
  Abstract: I will introduce a notion of coarse rigidity for \sigma-finite von Neumann algebras through modular derivations and their associated GNS-symmetric quantum Markov semigroups, extending Peterson’s framework of L2-rigidity to the nontracial setting.  For diffuse von Neumann algebras with separable predual, I will present a dichotomy result of the absence of amenable summands and rigidity in terms of central sequences. I will also discuss a few applications to Ozawa's solidity results for certain type III factors. This is joint work with Melchior Wirth.
  
  

• Xiao-Qi Lu (University of Glasgow, Scotland) 

Title: Hilbert transforms on Coxeter groups and groups acting on buildings
Abstract: Cotlar identities are a classical tool for proving the L_p-boundedness of the Hilbert transform on the real line for 1 < p < \infty. In 2017, Mei and Ricard generalized these identities to the noncommutative setting and established the L_p-boundedness of Hilbert transforms on free groups. In 2022, González-Pérez, Parcet, and Xia extended this approach to groups acting on R-trees using a geometric model. 

In this talk, we first establish the L_p-boundedness of Hilber transforms on Coxeter groups satisfying a certain nesting condition. We then extend these results to all finitely generated Coxeter groups and to groups acting on buildings that satisfy this condition. Our results provide the first examples of groups with property (FR) that admit L_p-bounded Hilbert transforms. This is a joint work with Runlian Xia.

October 13:

• Antonio López Neumann (Université Paris Cité, France)
  
  Title: Quantitative polynomial cohomology, lattices in rank 1 and measure equivalence.
  Abstract: Bader and Sauer initiated a systematic study of higher property T which has been particularly fruitful in the context of semisimple Lie groups and their lattices. In their work, the key point for understanding lattices is developing induction techniques for a polynomial version of group cohomology. Elaborating on this point, we introduce a quantitative version of polynomial cohomology and show that it computes usual group cohomology when certain filling functions satisfy polynomial bounds. We give two applications.

1) We obtain new vanishing results for non-uniform lattices in rank 1 simple Lie groups, and in particular we show that lattices in the exceptional Lie group F_4^{-20} have higher property T.

2) We show that Betti numbers of nilpotent groups are invariant by cobounded L^p-measure equivalence for large p.

This is based on joint work with Juan Paucar.

• Paolo Boldrini (Chalmers University, Gothenburg, Sweden)
  
  Title: Minimal actions without dynamical comparison.
  Abstract: Given an action of a countable group on the Cantor space, clopen subsets can be compared by cutting and moving through the action or by evaluating them on invariant measures. Dynamical comparison asserts that the measure-theoretic notion controls the dynamical one. Since its first appearance, dynamical comparison has been verified for a wide variety of actions. In joint work with Akshara Prasad, we constructed the first examples of topologically free minimal actions that fail dynamical comparison, and we showed that this phenomenon can occur both in the presence and in the absence of invariant measures.

October 6: 

• Max Carter (UC Louvain, Belgium)
  
  Title: Boundary representations and Wiener’s Tauberian for groups with a Gelfand pair.
  Abstract: It is a classical result of Norbert Wiener from the 1930’s, referred to as ``Wiener’s Tauberian theorem", that a function f in L1(Rd) generates a dense ideal if and only if its Fourier transform vanishes nowhere. Then, given a general locally compact group G, one can ask whether the Fourier transform on L1(G) also satisfies this property. In the case that this property holds for L1(G), G is called a ``Wiener group”. It was a classical question in Banach algebra theory during the 20th century to determine which groups are Wiener. It is a celebrated result in the area that compactly generated groups of polynomial growth and nilpotent groups are all Wiener groups. On the other hand, it is generally difficult to show that a group is not Wiener, and essentially the only known class of non-Wiener groups are connected semisimple Lie groups. In this talk I will discuss recent work where we show that many non-amenable totally disconnected locally compact groups are not Wiener, including reductive algebraic groups over non-archimedean local fields. The proofs make extensive use of representations of the given groups on their Furstenberg boundary.