Topological Quantum Groups, C*-Tensor Categories, and Subfactors

Concentration Week, July 27-31, 2020

Department of Mathematics, Texas A&M University - College Station, Texas, USA.

This concentration week is part of the Workshop in Analysis and Probability.

Overview:

The past two decades have seen spectacular developments in both the theory of operator algebraic (a.k.a. topological) quantum groups and the theory of von Neumann subfactors. These developments include Kustermans and Vaes' theory for locally compact quantum groups, approximation and rigidity properties for discrete quantum groups, subfactors, and related algebras algebras, a powerful classification program for the combinatorially defined ``easy quantum groups'', a rich theory of planar algebras with applications to the classification of small index subfactors, a representation theory for subfactors and related objects, and applications of both subfactors and quantum groups to quantum information science. In recent years it has become apparent that one of the fundamental mathematical structures underpinning many of these recent breakthroughs is that of a rigid C*-tensor category. Rigid C*-tensor categories provide a direct path between these two communities, allowing ideas developed by one community to be used to great effect by the other.

The aim of this concentration week is to bring together leading experts and young researchers working in both subfactors and operator algebraic quantum groups with the aim of fostering new communications and collaborations between these communities. We expect that many important mathematical problems in subfactors and quantum groups will benefit from input from both sides. As part of the concentration week, there will be four mini courses, several expository lectures, and ample time for informal discussions and collaborations.


Mini Courses:

Corey Jones (Ohio State U.) and David Penneys (Ohio State U.): Introduction to the classification program for subfactors.

Stefaan Vaes (K.U. Leuven): Property (T) for subfactors, rigid C*-tensor categories, and discrete quantum groups.

Christian Voigt (U. Glasgow): The Drinfeld double construction and complex semisimple quantum groups

Moritz Weber (U. Saarlandes): The classification program for easy quantum groups and tensor categories of partitions.


Invited Speakers:

  • Yuki Arano (Kyoto U.)
  • Dietmar Bisch (Vanderbilt U.)
  • Paramita Das (Indian Statistical Institute)
  • Yasayuki Kawahigashi (U. Tokyo)
  • Brent Nelson (Michigan State U.)
  • Claudia Pinzari (U. Roma 1)*
  • Julia Plavnik (Indiana U.)*
  • Dimitri Shlyakhtenko (UCLA)*
  • Matthias Valvekens (K. U. Leuven)
  • Roland Vergnioux (F. U. Berlin)


*=to be confirmed.

Financial Support: We expect to cover the local expenses (hotel/dorm accommodation and a modest per diem) for registered participants who request financial support. We are unable to cover travel expenses for most participants.


Organizing Committee:

Michael Brannan (Texas A&M University) and Makoto Yamashita (University of Oslo)