This event was 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 took place simultaneously at two locations: the Fields Institute in Canada and the International Centre for Mathematical Sciences (ICMS) in Edinburgh. This “twinned conference” model aimed to reduce the environmental impact of conference travel without sacrificing one-on-one interactions. The talks were hybrid, with the speaker giving an in-person talk at either Fields or ICMS that is streamed live to the other institute. The talks were held in the afternoons at ICMS and mornings at Fields. Minicourses were in person (not streamed) in the mornings at ICMS and in the afternoons at Fields. We There were two sets of minicourse speakers, one for each location.

At the time of this workshop, 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 was 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. The driving scientific goal of this workshop was 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 were 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, an open vibrant area in the intersection of operator algebras and tensor categories was created by bringing together two communities of researchers.