Orateur
Description
The concept of symmetries naturally arises in various areas of mathematics and science, including geometry, number theory, differential equations, and quantum mechanics. The more symmetries an object possesses, the better we can understand it through group-theoretic approaches.
Branching problems investigate how large symmetries break down into smaller ones, such as fusion rules, using mathematical formulations based on the language of representations and their restrictions. These problems have been studied for over 80 years. In recent years, there has been a surge of research focused on the restriction of continuous symmetries in infinite-dimensional cases, leading to the development of new geometric and analytic methods.
In my three lectures, I plan to provide an introduction to the branching problems of infinite-dimensional representations of real reductive groups, such as GL(n, R), using plenty of elementary examples to make the basic concepts and key ideas more accessible.
A major goal of my lectures is to capitalize on this momentum and bring together young students and postdocs from diverse mathematical disciplines, encouraging them to develop an interest in this promising field. If time permits, I will also present some open questions in the area.
