2026-T3 Operator Algebras: Approximation, Rigidity and Dynamics

September 14th to December 4th, 2026

Thematic trimester programme at the Institut Henri Poincaré, Paris

Operator algebras are self-adjoint subalgebras of the bounded operators on a Hilbert space and divide into two main classes: C∗-algebras and von Neumann algebras, according to whether one demands that they are closed in the norm topology or the weak operator topology. When one first meets these algebras, they might look quite similar, but they have different natures as exemplified by the commutative case: via the Gelfand transform, abelian C∗-algebras are algebras of continuous functions vanishing at infinity on a locally compact Hausdorff space, while abelian von Neumann algebras are essentially bounded measurable functions on a measure space. These flavours persist in general. Topological concepts such as dimension and invariants such as K-theory pervade the study of C∗-algebras, while measure- theoretic style methods are often used to study von Neumann algebras.

The long thematic program OA will focus on operator algebras and its still-evolving in- teractions with ergodic theory, topological dynamics, discrete subgroups of semisimple Lie groups, analytic, ergodic and geometric group theory, random matrices and quantum information theory.

Main scientific event:

The conferences and courses of this programme will also be accessible online.

September 14 to December 4, 2026: Operator Algebras: Approximation, Rigidity and Dynamics (IHP, Paris).

Introductory School:

September 14th to 18th:

Operator Algebras: Approximation, Rigidity and Dynamics at IESC (Cargèse)

Workshops:

• September 28 to October 2, 2026:
  Operator Algebras: Groups and Dynamics (IHP, Paris).
• October 26 to 30, 2026:
  Operator Algebras: Matricial Approximations (IHP, Paris).
• November 30 to December 4, 2026:
  Operator Algebras: Rigidity and Classification (IHP, Paris).

Organising committee:

• Cyril Houdayer (Ecole normale supérieure)
• Mikael de la Salle (CNRS, Université Claude Bernard Lyon 1)
• Stuart White (University of Oxford)

Scientific committee:

• Nadia Larsen (University of Oslo)
• Magdalena Musat (University of Copenhagen)
• Gilles Pisier (Sorbonne université & académie des sciences)
• Stefaan Vaes (KU Leuven)

Programme coordinated by the Centre Emile Borel at IHP

Sorbonne Université, CNRS