Bases for Cluster Algebras (22w5173)

The Casa Matemática Oaxaca (CMO) will host the "Bases for Cluster Algebras " workshop in Oaxaca, from September 25 - September 30, 2022.

The theory of cluster algebras emerged in the year 2000 as a combinatorial approach to study bases for quantum groups. Since then, commutative cluster algebras and their quantum deformations have been present in very diverse areas of mathematics and theoretical physics.

Constructing bases for both commutative and quantum cluster algebras and understanding their multiplicative structure is a meeting point of techniques and ideas from combinatorics, mirror symmetry, representation theory and quantum groups.

This topic has attracted the attention of distinguished mathematicians such as the Fields medalist Maxim Kontsevich and the 2018 Chern medalist Masaki Kashiwara. In the last 4 years there has been remarkable progress in the problem of constructing bases for cluster algebras and relating them to the canonical bases for quantum groups. Understanding the relation among these approaches is a difficult and important task that has been undertaken by various groups of researchers in recent years. This is a great moment to bring these groups together for a focused workshop on bases for cluster algebras.

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), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). The research station in Oaxaca is funded by CONACYT