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：The first half of this course gives a general introduction to p-adic Hodge theory. The second part discusses recent topics, including the Fargues-Fontaine curve and p-adic period domains.Prerequisite：Algebraic number theory and algebraic geometryReference：Laurent Fargues and Jean-Marc Fontaine. Courbes et fibrés vectoriels en théorie de Hodge p-adique. Astérisque (406).Jean-Franç...
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