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#### Topics in random matrix theory

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...

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#### Introduction to geometric representation theory

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

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