Non-Classical Constructions in Tensor Categories and Conformal Field Theory (22frg002)
Organizers
Andrew Schopieray (University of Alberta)
Terry Gannon (University of Alberta)
Julia Plavnik (Indiana University)
Description
The Banff International Research Station will host the "Non-Classical Constructions in Tensor Categories and Conformal Field Theory" workshop in Banff from November 20, 2022 to December 4, 2022.
Just as general science cannot proceed without evidence and experimentation, the mathematical sciences cannot proceed without a robust set of examples to make observations, and test conjectures upon. In the 1980's, inspired by mathematical physics, mathematicians were developing what would become the definition of tensor, fusion, and modular tensor categories. These mathematical objects require copious amounts of data to describe, which is a reflection of their initial inspirations from conformal field theory, but also of their application to diverse fields such as invariants of knots and links, vertex operator algebras, and von Neumann algebras, to name a few. Almost all known examples of these fundamental mathematical objects come from classical families that have been known since the genesis of the field, and a small number of classical constructions to create new examples from the old. A finite list of "exotic", or non-classical examples have been found though, for which there is no known connection to classical examples using known constructions. Evans \& Gannon, and subsequently Grossman \& Izumi have proposed the existence of infinite families of non-classical examples, and on a combinatorial/number-theoretic level these non-classical examples can be constructed from classical examples using a yet-to-be-described amalgamation construction. Our focused research group, drawn from a diverse collection of experts in complementary fields of study, aims to describe the mathematical underpinnings of this construction to bring about a new and non-classical era in the study of tensor categories and related fields.
The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).
Just as general science cannot proceed without evidence and experimentation, the mathematical sciences cannot proceed without a robust set of examples to make observations, and test conjectures upon. In the 1980's, inspired by mathematical physics, mathematicians were developing what would become the definition of tensor, fusion, and modular tensor categories. These mathematical objects require copious amounts of data to describe, which is a reflection of their initial inspirations from conformal field theory, but also of their application to diverse fields such as invariants of knots and links, vertex operator algebras, and von Neumann algebras, to name a few. Almost all known examples of these fundamental mathematical objects come from classical families that have been known since the genesis of the field, and a small number of classical constructions to create new examples from the old. A finite list of "exotic", or non-classical examples have been found though, for which there is no known connection to classical examples using known constructions. Evans \& Gannon, and subsequently Grossman \& Izumi have proposed the existence of infinite families of non-classical examples, and on a combinatorial/number-theoretic level these non-classical examples can be constructed from classical examples using a yet-to-be-described amalgamation construction. Our focused research group, drawn from a diverse collection of experts in complementary fields of study, aims to describe the mathematical underpinnings of this construction to bring about a new and non-classical era in the study of tensor categories and related fields.
The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).
