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Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

The symmetries of classical mathematical objects form a group. In the past several decades, we have seen new quantum mathematical objects like von Neumann algebras and quantum field theories whose symmetries are best described by tensor categories. One reason for this is that these mathematical objects naturally form higher categories, and thus their endomorphisms naturally form higher monoidal categories. In this sense, we view fusion categories as objects which encode quantum symmetries. Subfactors are a rich source of examples of exotic unitary fusion categories, and conversely, every unitary fusion category arises from a subfactor. This correspondence leads to deep mathematical connections between these fields. These mathematical objects are also intimately related to conformal field theory and topological phases of matter, which give topological quantum field theories, in which higher categories play an important role. The purpose of this workshop is built on the 2014 and 2018 BIRS workshops on subfactors and fusion categories, with the goal of studying these objects through a higher categorical lens. To do so, we will bring together world experts from subfactors, fusion categories, higher categories, and mathematical physics to further develop the deep and rich connections between these fields.

In this workshop we will study infinite-type surfaces and their mapping class groups from several perspectives. Each participant will be asked to either give a lecture or run a problem session.

Geometry and Topology,    Algebra

Fields Institute

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Courses and Events for Math Students and Early Career Researchers,    Algebra

Banff International Research Station (BIRS) for Mathematical Innovation and Discovery

Courses and Events for Math Students and Early Career Researchers,    Algebra

The Fields Institute for Research in Mathematical Sciences

This intensive graduate school will cover topics central to the Workshop on Interactions between Group Theory and Homotopy Theory the following week. This school is designed to give graduate students and early career researchers in related fields a better understanding of each subject, thus enabling the participants to better engage in the subsequent workshop.

Geometry and Topology,    Courses and Events for Math Students and Early Career Researchers

The Fields Institute for Research in Mathematical Sciences

Group theory and topology have a long and rich history of interaction. This workshop will bring together experts working on different aspects of this interaction in order to share ideas and boost the development of new methods that can be applied to the topology of configuration spaces, braid groups, mapping class groups and manifolds, and spaces of commuting elements.

Geometry and Topology,    Courses and Events for Math Students and Early Career Researchers