Affine algebras and representation theory

Representation theory is a broad area of mathematics connecting number theory, geometry, analysis and mathematical physics. This workshop will bring together a critical mass of researchers working on several aspects of representation theory which are particular strengths of Japanese mathematics and closely connected to current work at OIST.

One focus will be the categorification of affine Kac–Moody algebras and related quantum groups, developed through the work of Khovanov, Lauda, Rouquier, Kashiwara and many others. This subject has become a central tool in modern representation theory, with applications to crystal bases, canonical bases, cluster algebras, geometric representation theory, and modular representations of finite groups. The combinatorial and categorical aspects of this area are represented at OIST through the Representation Theory and Algebraic Combinatorics Unit.

A second theme will be vertex operator algebras, W-algebras and their connections with affine Kac–Moody algebras. In recent years these subjects have seen renewed interaction with high-dimensional quantum field theory, including the AGT correspondence, 4D/2D dualities, and the appearance of W-algebras in the quantum geometric Langlands program. These topics provide a natural bridge between algebra, geometry and mathematical physics.

A third direction will be Coulomb branches and related geometric approaches to representation theory. The mathematical theory of Coulomb branches has provided new algebras and categories linking quiver varieties, finite W-algebras, Yangians, and the representation theory of Lie algebras in positive characteristic. This direction has strong connections to the work of researchers in Japan and to international developments in geometric representation theory.

Our workshop will also include a keynote lecture by Geordie Williamson on artificial intelligence and mathematics. The lecture will be designed for a broad OIST audience and will discuss how modern AI and machine-learning tools can support mathematical intuition, conjecture generation, experimentation and proof discovery. This addition will broaden the appeal of the workshop beyond representation theory while remaining scientifically integrated: Williamson's own work is a leading example of the interaction between representation theory, geometry and machine learning.

The expected benefits to OIST are substantial. The workshop will strengthen OIST's visibility as a mathematical hub in Asia and will bring leading researchers from Japan, the rest of Asia, Europe, North America and Oceania to campus. It will directly benefit the Chiral Representation Theory Unit and the Representation Theory and Algebraic Combinatorics Unit, while also creating points of contact with OIST researchers interested in mathematical physics, geometry and algebra. In particular, we expect several research talks to be of interest to members of  the Gravity, Quantum Geometry and Field Theory Unit (Toriumi) and the Algebraic Combinatorics and Fundamental Physics Unit (Parisi). The keynote lecture should have even broader interest throughout the OIST community.

Talks will be open to OIST graduate students and postdocs, and contributed talks and lightning talks will be used to involve early-career researchers. The workshop will help build connections between OIST and major international centers in mathematics and will increase awareness of OIST among strong potential postdoctoral fellows, PhD applicants and future faculty candidates.

*OIST members are welcome to attend all scientific sessions. Meals are closed sessions for registered participants only.

Workshop website: https://www.oist.jp/conference/affine-algebras-and-representation-theory

OIST is deeply committed to the advancement of women in science, in Japan and worldwide. Women are strongly encouraged to apply.