北京雁栖湖应用数学研究院

The conference will be held at the Beijing Institute of Mathematical Sciences and Applications from Monday July 8 to Friday July 12, 2024, as a satellite conference of the International Congress of Basic Science.

World experts and early-career researchers will come together to exchange ideas and to build research networks.

Representation theory is a prominent branch of mathematics which studies abstract algebraic structures by relating them to well-understood ones, traditionally linear maps on a vector space. It connects to many other branches (category theory, combinatorics, harmonic analysis, geometry, topology, number theory, ...) and as such plays a major role in unified frameworks such as the Langlands program.

One of the important applications of representation theory and indeed one of its orgins is the study of symmetries in physical models. Classical or quantum integrable systems can be regarded as dynamical systems with “maximal” symmetry. In classical mechanics, integrability means a sufficient number of independent integrals of motion, and quantum integrability has a similar meaning. Sometimes integrable systems, especially infinite-dimensional ones, make it possible to study effects that are usually masked by complicated chaotic dynamics in non-integrable systems. Quantum integrable systems also inspired the discovery of new algebraic structures, such as quantum groups.

Together, representation theory and integrable systems form a modern and powerful area of science at the interface of pure mathematics and applications.