Peng Shan- On Geometrical Realization of Centers

This course explores the geometrical realization of centers in algebra, with a focus on the links between representation categories and singular cohomology of algebraic varieties. By reviewing examples and explaining connections between the center of small quantum groups and the cohomology of certain affine Springer fibers, learners will gain insights into this important invariant. The course covers topics such as quantum groups, deformation, compatibility, and admissible representations, making it suitable for individuals interested in Lie theory, algebra, and mathematical structures. The teaching method involves a lecture format with theoretical explanations and examples to illustrate key concepts.