Abstract

Symmetries appear naturally in various areas of mathematics and the sciences, ranging from geometry, numbers, differential equations to quantum mechanics. The more symmetries there are, the better we can grasp the objects by group theoretic approaches. Branching problems investigate how a 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 focus- ing 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 (conjecturally) unified phenomenon. 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.