Interactions of Geometric and Quantum Topology focused on Links in Thickened Surfaces (25w5497)


Hans Boden (McMaster University)

Patricia Cahn (Smith College)

Efstratia Kalfagianni (Michigan State University)

Ilya Kofman (College of Staten Island & The Graduate Center, CUNY)

Alice Kwon (SUNY Maritime College)


The Banff International Research Station will host the “Interactions of geometric and quantum topology focused on links in thickened surfaces” workshop in Banff from April 13 - 18, 2025.

This workshop will highlight new results in knot theory and low-dimensional topology coming from a wide range of geometric and topological methods. Knot theory is an active research area of mathematics, which is closely connected with mathematical physics, and many results are of interest to biologists. Low-dimensional topology studies the global properties of geometric spaces in dimensions 2, 3 and 4, such as 3-dimensional space and 4-dimensional space-time. Some of this research is motivated by a deep open problem: how to bridge the chasm between quantum and geometric topology. Thurston established the importance of geometric invariants, especially hyperbolic volume, in low-dimensional topology. A revolution in knot theory was ushered in with the discovery of the Jones polynomial in 1984, which led to vast families of quantum invariants. A major research goal is to establish relationships between quantum invariants of a knot, such as the Jones polynomial, and the geometry of the knot complement. Much of the recent progress in this very active area of mathematics makes use of the interplay between sophisticated mathematical invariants (quantities that can be used to distinguish one space from another) coming from geometry, topology and knot theory. The workshop will focus on invariants of links in thickened surfaces, featuring new discoveries on the shape of space and knotted objects inside space, and will host leading experts from around the world. This event is organized by Professors Patricia Cahn of Smith College, Hans Boden of McMaster University, Effie Kalfagianni of Michigan State University, Ilya Kofman of the City University of New York, and Alice Kwon of the State University of New York.

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), and Alberta’s Advanced Education and Technology.