Description

Analytic group theory is an area focused on using analytic techniques for the study of infinite groups. The field can be thought of as beginning with work of Mostow, Furstenberg and Margulis on rigidity and super- rigidity for discrete subgroups of Lie groups, where their work used ideas from ergodic theory, functional analysis, probability, representation theory and quasi- conformal analysis. Soon after that work, mainly motivated by work of Alain Connes, similar ideas began to appear in the theory of operator algebras particularly when studying group and group action von Neumann algebras. A more geometric, but still analytic, set of approaches were spelled out in various works of Gromov, culminating in his book on Asymptotic Invariants of infinite groups. These three threads have been interwoven in much research on infinite groups over the past 40 years.

Over the last decade or so, these techniques have mixed with each other giving rise to an even richer theory, so much so that the scope has become rather large. We shall therefore focus on a few specific themes that add focus and gel with the theme in Section 5.1. We shall particularly be interested in analytic, ergodic theoretic and operator algebraic tools applied to geometric group theory. The following is a sample of sub-themes that are likely to be relevant during the semester.

  1. Measurable group theory and l2 invariants
  2. Amenability and amenable actions
  3. Property T for groups and von Neumann algebras
  4. Commensurators
  5. Rigidity of groups, actions and operator algebras

Programme Activities

Semester-Long Activities

Throughout the semester, the programme will feature:

  • Weekly mini-courses
  • Weekly research seminars
  • Weekly "what is?" seminar series, run by young researchers and postdocs
  • Regular coffee-time sessions for informal knowledge-sharing and collaboration
  • A two-week introductory school in August with exercise sessions, accessible to participants of both parallel programmes

Intensive Programmes

1. Introductory School (shared with Surface Group Representations programme) August 10 – August 21, 2026

A two-week school structured across two weeks. Week 1 runs in the style of an Arbeitsgemeinschaft, participants work in smaller groups on introductory material and present to each other. Week 2 consists of mini-courses on more advanced aspects of the introductory topics. The school is accessible to graduate students and postdocs and open to participants of both programmes.


2. Major Concentration Period 1: Groups, Property (T), and Expansion October 5 – October 23, 2026

  • Week 1: Mini-courses
  • Week 2: Research conference
  • Week 3: Advanced mini-courses

3. Major Concentration Period 2: Group von Neumann Algebras and C-algebras November 9 – November 27, 2026

  • Week 1: Mini-courses
  • Week 2: Research conference
  • Week 3: Advanced mini-courses

ORGANISERS

Indira Chatterji

Côte d’Azur University

Srivatsav Kunnawalkam Elayavalli

University of Maryland

David Fisher

Rice University, Texas

Mikołaj Frączyk

Jagiellonian University

Mehrdad Kalantar

University of Houston

Nicolas Monod

École Polytechnique Fédérale de Lausanne

Roman Sauer

Karlsruhe Institute of Technology