# Group Operator Algebras: Classification, Structure and Rigidity (24w5174)

## Organizers

Adrian Ioana (University of California, San Diego)

Ionut Chifan (The University of Iowa)

Cyril Houdayer (Université Paris-Saclay)

Matthew Kennedy (University of Waterloo)

Tatiana Shulman (University of Gothenburg)

## Description

The Banff International Research Station will host the “Group Operator Algebras: Classification, Structure and Rigidity” workshop in Banff from September 22 - 27, 2024.

Operator algebras are collections of certain infinite matrices, called Hilbert space operators. They were originally introduced in the 1920s in order to formalise quantum mechanics and understand representation theory of groups. Operator algebras (C$^*$-algebras and von Neumann algebras) arise naturally from representations of groups as unitary operators on a Hilbert space. A fundamental problem is to classify and investigate the structure of these so-called group operator algebras.

The workshop will focus on this problem and related applications of operator algebras to groups and their representations. This is a broad and exciting research program, which has deep interactions with several areas of mathematics including (geometric and measured) group theory, ergodic theory and topological dynamics. The workshop will build on these connections and recent spectacular developments to generate further interaction and progress.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada’s Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta’s Advanced Education and Technology, and Mexico’s Consejo Nacional de Ciencia y Tecnología (CONACYT).