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

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 summer school and workshop 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 program, there will be six mini courses, several expository lectures, and ample time for informal discussions and collaborations.

PLEASE NOTE: This event at Waterloo immediately precedes the 50th Canadian Operator Symposium, which will take place at the University of Ottawa, May 30-June 3, 2022. Participation in both events is highly encouraged! In order to encourage participation in both meetings, we plan to arrange group transportation from Waterloo to Ottawa on Sunday May 29. (Details forthcoming.)

Mini Courses:

Corey Jones (North Carolina State U.) : Braided tensor categories in operator algebras.

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

Julia Plavnik (Indiana U.): Introduction to modular tensor categories and their applications.

Stefaan Vaes (K.U. Leuven): Property (T) discrete quantum groups associated with highly symmetric graphs.

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:

• Jason Crann (Carleton U.)

• Paramita Das (Indian Statistical Institute)

• Yasayuki Kawahigashi (U. Tokyo)

• Mehrdad Kalantar (U. Houston)

• Brent Nelson (Michigan State U.)

• Emily Peters (Loyola U. Chicago)

• Simon Schmidt (Copenhagen)

• Dimitri Shlyakhtenko (UCLA)

• Roland Vergnioux (U. Caen)

Contributed Talks:

• Benjamin Anderson-Sackaney (University of Waterloo)

• Quan Chen (The Ohio State University)

• Daniel Gromada (Czech Technical University)

• Roberto Hernandez-Palomares (Texas A&M University)

• Srivatsav Kunnawalkam Eleyavalli (Vanderbilt University)

• Junichiro Matsuda (Kyoto University)

Financial Support: We have applied for funding to enable us to cover local expenses (hotel/dorm accommodation) for registered participants who request financial support. Priority will be given to junior participants (graduate students and postdocs). We do not expect to be able to cover travel expenses for most participants.

Organizing Committee:

Michael Brannan (University of Waterloo) and Makoto Yamashita (University of Oslo)