2026 Mini Workshop on Equivariant TQFT

About

• Location: Purdue University, in West Lafayette, IN
• Dates: Monday, June 8, 2026 through Wednesday, June 10, 2026
• Organizers: Colleen Delaney, Carmen Rovi, Eric Samperton
• Local organizers: Gordon Li, Philip Rehwinkel
• Participants who expect to travel by air might consider flying into Indianapolis International (IND), Purdue University (LAF), or Chicago O'Hare (ORD), depending on which is most sensible.

This mini workshop will focus on aspects of topology, algebra, category theory, and quantum computing that arise from equivariant topological quantum field theories, especially in dimensions 2+1 and 3+1. The event is a follow-up to a prior 5-Day Workshop at BIRS Casa Matematica Oaxaca on Equivariant TQFT.

We thank the National Science Foundation for supporting the event through NSF DMS 2530723.

Schedule

The precise schedule is TBD, but we will have at least the following talks (click titles to see abstracts):

• Equivariant higher vector spaces, Alexei Davydov (Ohio University)

  Higher categories of higher vector spaces naturally form what is now called a categorical spectrum. Homotopy groups of this categorical spectrum are very non-trivial and interesting for applications. We examine their behaviour under the "change of base". One example of such change of base is passing from vector spaces to their equivariant versions.

• Complex Chern-Simons invariants via the Reshetikhin-Turaev construction, Calvin McPhail-Snyder (Duke University)

  The Chern-Simons invariant \(\tau\) of a flat \(\mathfrak{sl}_2(\mathbb{C})\) connection on a 3-manifold (equivalently, a generalized hyperbolic structure) is an important geometric invariant that can be understood as a complexification of the hyperbolic volume. Because it is defined using an integral it is natural to expect it can be computed via cutting and gluing, as in a TQFT; this is well-understood for ideal triangulations. In this talk I will explain how to compute \(\tau\) for tangle exteriors using the Reshetikhin-Turaev formalism and how this naturally leads to a quantization of \(\tau\) that generalizes Kashaev's invariant. This perspective suggests the existence of a \(SL_2(\mathbb{C})\)-crossed braided tensor category capturing \(\tau\) and its quantization, and I will indicate what is known and what remains to be worked out. Parts of this talk are based on joint work with N. Reshetikhin.
• The Grothendieck ring of module categories over a braided fusion category, Dmitri Nikshych (University of New Hampshire)

  This is a report on a joint work with Riley Chinburg.

  For a non-degenerate braided fusion category \(B\), we show that the Grothendieck \(Z_+\)-ring of \(B\)-module categories admits a canonical filtration indexed by the partially ordered set of localizations of B. We investigate the resulting filtered ring in several concrete examples and describe the associated graded structure. In particular, we show that the complexified algebra of module categories is not semisimple in general.