Skew Braces, Braids and the Yang-Baxter Equation (24w5201)


Leandro Vendramin (Vrije Universiteit Brussel)

(University of Exeter)

Julia Plavnik (Indiana University)

(Texas A&M University)


The Banff International Research Station will host the “Skew Braces, Braids and the Yang-Baxter Equation” workshop in Banff from May 5 - 10, 2024.

The YBE originates in statistical mechanics in studying models known as integrable systems from the late 1960s and 1970s. Despite its somewhat technical beginnings, it soon spawned critical new ideas and whole areas of research. Quantum groups, quantum topology, and topological quantum field theory all owe much to the YBE. Indeed, the work cited for 3 of the 4 1990 Fields medalists' is deeply interwoven with the YBE. In the intervening years, the interest in the YBE has not waned as new applications and connections are discovered.

Although the equation can now be regarded as classical, we know very little about the full landscape of its solutions. Several independent research groups have developed some promising ideas for making progress on both the classification problem and on interesting new applications. This workshop brings together these disparate groups for a week to exchange ideas and initiate new collaborations on projects surrounding the YBE.

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).