This event will be a twinned transatlantic conference on “C*-algebras and tensor categories”, promoting new connections between C*-algebra theory and tensor categories/subfactors - an interface with tremendous, yet barely explored, potential.

The conference takes place simultaneously at two locations: the Fields Institute in Canada and the International Centre for Mathematical Sciences (ICMS) in Edinburgh. This "twinned conference'' model aims to reduce the environmental impact of conference travl without sacrificing one-on-one interactions. The talks will be hybrid, with the speaker giving an in-person talk at either Fields or ICMS that is streamed live to the other institute. The talks will be held in the afternoons at ICMS and mornings at Fields. Minicourses will be in person (not streamed) in the mornings at ICMS and in the afternoons at Fields. We have two sets of minicourse speakers, one for each location, who will coordinate their lectures.

Many major 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. The overarching objective of this conference 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. Our driving scientific goal is the question: Which strongly amenable rigid C*-tensor categories act on which classifiable C*-algebras, and when can such actions be reasonably classified?

Due to the recent success in the C*-algebra classification program, 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. This is the right moment to lay the foundations for large-scale research into quantum symmetries on C*-algebras.

The main techniques will be drawn both from deep classification theorems in subfactor theory, including the theorems of Jones and Ocneanu from the '80s and Popa from the '90s, and the rapid recent progress in the classification of C*-algebras. Through this twinned workshop, we aim to open a vibrant area in the intersection of operator algebras and tensor categories, and bring together two communities of researchers. 

Sponsors

• K-Theory Foundation

Mini-Courses

Mini-Course on C*-Algebras and Classification

Instructors:

• José Carrión, Texas Christian University
• Chris Schafhauser, University of Nebraska-Lincoln

Schedule:

• Day 1: Statement and context of the classification theorem, including a discussion of the hypotheses. Relationship between classification of algebra and classification of morphisms.
• Day 2: The Jiang-Su algebra; consequences of Jiang-Su stability; intertwining by reparameterization.
• Day 3: Some aspects of KK-theory including absorption and the non-stable theory.
• Day 4: Strategy behind equivariant classification: cocycle conjugacy, cocycle morphisms, equivariant intertwining arguments.
• Day 5: Actions of finite groups with the Rokhlin property.

Mini-Course on Tensor Categories

Instructors:

• Roberto Hernández Palomares, University of Waterloo
• Qing Zhang, University of California, Santa Barbara

Schedule:

• Day 1: Motivation: from Connes to Jones, and what to look at around the C*-classification program. Tensor categories (by example).
• Day 2: Unitarity and rigidity in TCs and resulting graphical calculus.
• Day 3: Invariants for fusion categories and inclusions of C*-algebras (Index theory and their representation categories).
• Day 4: Module categories, Q-systems, and Morita equivalence. Applications: the standard invariant of an inclusion.
• Day 5: C*-quantum dynamics and examples. Time allowing: classification framework, examples, and perspectives.

Plenary Speakers

• Anshu, The Fields Institute
• Yuki Arano, Nagoya University
• Michael Brannan, University of Waterloo
• Paramita Das, Indian Statistical Institute, Kolkata
• Anna Duwenig, Katholieke Universiteit Leuven
• Jamie Gabe, University of Southern Denmark
• Elizabeth Gillaspy, University of Montana
• Masaki Izumi, Kyoto University
• Xin Li, University of Glasgow
• Ying-Fen Lin, Queen's University Belfast
• Melody Molander, University of California, Santa Barbara
• Zhuang Niu, University of Wyoming
• Ulrich Pennig, Cardiff University
• Sarah Reznikoff, Virginia Tech
• Mikael Rørdam, University of Copenhagen
• Stefaan Vaes, Katholieke Universiteit Leuven
• Christian Voigt, University of Glasgow
• Dilian Yang, University of Windsor