Equivariant Topological Quantum Field Theory (25w5402)


Carlos Segovia (CONACYT-UNAM-Oaxaca)

Colleen Delaney (UC Berkeley)

Carmen Rovi (Loyola University Chicago)

Eric Samperton (Purdue University)

Bernardo Uribe (Universidad del Norte)


The Casa Matemática Oaxaca (CMO) will host the "Equivariant Topological Quantum Field Theory" workshop in Oaxaca, from September 7 to September 12, 2025.

A topological quantum field theory (TQFT) is a kind of mathematically rigorous quantum field theory in which the behavior of a physical system is independent of the geometry of the manifolds (that is, ``spaces" and ``spacetimes") on which the system resides. TQFTs come in many different flavors, and both physicists and mathematicians are interested in classifying all of them. To this end, some of the most important TQFTs are the ones that exhibit \emph{symmetries}. These are called "equivariant TQFTs," and will be the central objects of study in this 5-day workshop.

The main goal of the workshop is to attack problems and develop mathematical applications involving equivariant TQFTs. Efforts will be focused on two complementary tracks, but with an eye towards cross-pollination of the methods of each. The first track will comprise quantum algebraic techniques such as quantum groups, tensor categories, gauging, (de-)equivariantization, orbifolding and zesting; the second track will build on methods of equivariant topology, especially equivariant bordism. A secondary goal of the workshop is to further refine the applications of equivariant TQFTs to physics, for example, in condensed matter physics (where equivariant TQFTs provide a framework for studying symmetry-enriched quantum phases of matter), in high energy physics (where it has recently been understood that TQFTs provide a powerful language for describing global categorical symmetries), or in quantum computation (where TQFTs and tensor categories offer a useful perspective on error-correction and fault tolerance).

This workshop aims to catalyze significant near-term developments by uniting experts from across all of the subfields interacting with equivariant TQFT, as well as to contribute to the long-term viability of the subject by training the next generation of students. Particular emphasis will be placed on strengthening research and mentorship relationships across the Americas.

The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide 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 in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF) and Alberta's Advanced Education and Technology.