Actions of Tensor Categories on C*-algebras

January 21 - 28, 2021

Overview

ATC2021 ImageNote: This workshop will be held on Thursday-Friday, January 21-22, 2021 and Monday-Thursday, January 25-28, 2021

Virtual Workshop: In response to COVID-19, all participants will attend this workshop virtually via Zoom. Workshop registrants will receive the Zoom link a few days prior to the workshop, along with instructions on how to participate. The video of the recorded sessions will be made available on IPAM website.

Classical group actions on spaces can be viewed as symmetries of the corresponding operator algebra of continuous or measurable functions on the space. This vastly generalizes to quantum symmetries on non-commutative spaces. The underlying space is replaced by a non-commutative operator algebra, and the group action by the more general notion of symmetry via tensor categories.

Many major recent breakthroughs in the classification of C*-algebras of finite topological dimension have been underpinned by the large scale transfer of von Neumann techniques on multiple levels. Today C*-algebras stand at exactly the analogous stage to where von Neumann algebra theory was around the early ’80s when Jones’ pioneered subfactor theory.

The overarching objective of this workshop is to bring together researchers at the interface of the rapidly developing areas of the structure and classification of C*-algebras and subfactor theory/tensor categories. Advanced minicourses (Jan 21-22) will enable a rich dialogue between the two communities, and participants will leave with many new problems to explore, as well as deeper insights about how C*-algebraic and von Neumann algebraic techniques interact.

Organizing Committee

David Penneys (Ohio State University, Mathematics)
Emily Peters (Loyola University, Chicago)
Aaron Tikuisis (University of Ottawa)
Stuart White (University of Oxford)