报告人：徐晓濛，北京大学国际数学研究中心

时间: 2024年5月10日，9：45

地点：东区第五教学楼407教室

题目: An introduction to the Stokes phenomenon and isomonodromy deformation

摘要: This talk gives an introduction to the Stokes matrices of a linear meromorphic system, and the associated nonlinear isomonodromy deformation equation. In the case of Poncare rank 1, the nonlinear equation naturally arises from the theory of Frobenius manifolds, stability conditions, Poisson geometry, representation theory and so on, and can be seen as a higher rank generalizations of the sixth Painlevé equation.

时间: 2024年5月10日，14：00

地点：东区第五教学楼206教室

题目1: Solving the isomonodromy equation via the Riemann-Hilbert method

摘要1: This talk solves the isomonodromy equation, in the sense that it gives a parameterization of the asymptotics of the solutions of the isomonodromy equation at a critical point, the explicit formula of the monodromy/Stokes matrices of the linear problem, as well as a connection formula between two differential critical points. As an application, the regularized limits of Stokes matrices are given. It is partially based on a joint work with Qian Tang.

题目2: The WKB approximation in the Stokes phenomenon and Cauchy interlacing inequality

摘要2: This talk studies the WKB approximation of the linear meromorphic systems of Poncaré rank 1, via the isomonodromy approach. It unveils a relation between the WKB approximation of the Stokes matrices, the Cauchy interlacing inequality and cluster algebras. It is based on a joint work with Anton Alekseev, Andrew Neitzke and Yan Zhou.

时间: 2024年5月11日，8：30

地点：东区第五教学楼502教室

题目: Quantum Stokes phenomenon and quantum irregular Riemann-Hilbert map

摘要: This talk introduces the universal quantum linear ordinary differential equations at an arbitrary order pole. It then proves that the quantum Stokes matrices, of the differential equation at a k-th order pole, give rise to an associative algebra, that quantize the Poisson structure on the moduli space of meromorphic connections at a k-th order pole.  In the case k=2, the associative algebra involved is the Drinfeld-Jimbo quantum group. Our results give a dictionary between the Stokes phenomenon at 2nd order pole and the representation theory of quantum groups, including at the roots of unit, the Gelfand-Testlin, crystal basis and so on.