Description: This course will give a brief introduction to random matrix theory. Some topics we plan to cover are: Wigner semicircle law, the moment method, the resolvent method, invariant ensembles, Wigner matrices, sample covariance matrices, bulk universality, edge universality, rigidity of eigenvalues, Dyson Brownian motion, Tracy-Widom law, and free probability.Prerequisite:Probability, S...
Description: This will be an introductory course to the geometric representation theory. We will mainly focus on the book of Chriss and Ginzburg.Prerequisite:Some knowledge of Lie algebra, Lie group and algebraic geometryReference:N. Chriss and V. Ginzburg, Representation theory and complex geometryV. Ginzburg, Geometric methods in the representation theory of Hecke algebras and quantum group