Peng Shan- On Geometrical Realization of Centers

Explore a 42-minute lecture by Peng Shan on the geometrical realization of centers in algebra, presented at the International Mathematical Union. Delve into the intriguing connections between the center of representation categories in Lie theory and the singular cohomology of algebraic varieties. Examine various examples illustrating these links and discover a novel connection between the center of small quantum groups and the cohomology of certain affine Springer fibers. Follow along with the comprehensive syllabus, covering topics such as Springer resolutions, affine Springer fibers, quantum groups, deformations, and compatibility. Gain insights into ongoing work on modular analogs and the relation to TOFT, as well as admissible representations and elliptic fibers.

Intro
Table of contents
Cohomology
Theme
Springer resolution
Relation to the center
Affine Springer fibers elliptic and split
Our setting
Quantum groups
The small quantum group
Deformation of
The center of
Compatibility
Dimension estimation
Further remarks
Modular analog (work in progress)
Relation to 34 TOFT
Admissible representations and eliptic fiber
Other examples