Infinite-dimensional Lie algebras and affine quantum groups

Prerequisite You should be familiar with fundamental notions in algebra and representation theory (basic ring theory, associative algebras, Lie algebras and their universal enveloping algebras

Isomonodromic deformations and tau functions

Prerequisite basic knowledge of function of one complex variable, algebraic topology, compact Riemann surface Abstract I will talk about a general theory of monodromy preserving deformation, which ...

Geometry of Discrete Integrable Systems and Painlevé Equations

Prerequisite The course is designed to be essentially self-contained, but some background in higher-level mathematics is expected. Specifically, we need some basic results from Linear Algebra

Torsion theorem of the zero of a certain Kodaira-Spencer morphism over P^1 removing four points

Abstract In this talk, I shall explain a torsion theorem to the effect that the unique zero of the Kodaira-Spencer map attached to a certain quasi-semistable family of complex projective varieties

求真大讲堂预告 | 第三十一讲：声波增雨数学力学问题

主讲人介绍 王光谦，中国科学院院士，现任清华大学副校长、全国政协常委、民盟中央常务副主席。主要从事水沙科学与江河治理研究。在水沙运动理论方面，建立了水沙两相流的动理学模型，提出了泥沙颗粒的浓度与速度...

Lagrangian correspondence and its application to Floer theory

Eigenvarieties, families of Galois representations, p-adic L-functions

Prerequisite Basic commutative algebra, algebraic geometry, algebraic number theory Abstract This course is intended to give a gentle introduction to p-adic families of modular forms and p-adic

Certifiable Outlier-Robust Geometric Perception

Abstract I will present an overview of the theory of quantitative homogenization for elliptic and parabolic equations, with an emphasis on the "coarse-graining" point of view. I will begin by tryin...

Solving quantum field theory

Abstract We explain how to solve quantum field theories (or renormalization group flows). (We assume little preliminary knowledge; I am planning to explain in a way accessible to advanced high-scho...

From exceptional sets to non-free sections

Abstract Manin’s conjecture is a conjectural asymptotic formula for the counting function of rational points on Fano varieties over global fields. With Brian Lehmann, I have been studying exceptio...