In the IHP Trimester on Operator Algebras in Paris, there is a Junior Seminar being organised jointly by Felipe Flores, Shanshan Hua and myself. The seminar will run on Tuesday afternoons at 14h on the following dates: October 6, 13, 20 and November 3,10,17, 24. There will be two talks of 45 minutes with a break in between on all of these days. The talks will take place at the Ampitheatre Darboux at the Institut Henri Poincaré.
You can find the program, the title and abstracts here.
October 13:
Antonio López Neumann (Université Paris Cité, France)
Paolo Boldrini (Chalmers University, Gothenburg, Sweden)
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.
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.