Branching Problems for Representations of Real, P-Adic and Adelic Groups (24w5220)

The Banff International Research Station will host the “Branching problems for representations of real, p-adic and adelic groups” workshop at the UBC Okanagan campus in Kelowna, B.C., from July 7 - 12, 2024.

Workshop slides: Click here to access

Symmetries appear naturally in various areas of mathematics and the sciences, ranging from geometry, numbers, differential equations to quan- tum mechanics. The more symmetries there are, the better we can grasp the objects by group theoretic approaches.

Branching problems investigate how large symmetries break down into smaller ones, such as fusion rules, via a mathematical formulation using the language of representations and their restrictions. Branching problems have a history of study of over 80 years. In recent years there was an outburst of research activities focusing on the restriction of continuous symmetries in the infinite-dimensional cases, for which new geometric and analytic methods have been developed. We highlight branching problems of infinite-dimensional representations of real, p-adic and adelic reductive groups, the former carrying analytic features and the latter carrying number-theoretic features, which might lead us to a (conjectural) unification of phenomena.

A major goal of the Workshop is to capitalize on this momentum and to gather researchers from diverse mathematical disciplines to encourage new collaborations, and achieve progress in solving open questions in number theory, geometry and physics.

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. BIRS 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).