北京雁栖湖应用数学研究院

李镛 , 唐鑫星 , 王路瑶

唐鑫星

2025年11月29日 14:00 至 16:00

A3-3-301

Zoom 442 374 5045 (BIMSA)

In this talk we use the Pearcey integral as a model example to illustrate exact WKB analysis in a genuinely multivariable setting. we first derive the holonomic system of partial differential equations (the Pearcey system) that it satisfies, and explain how this system defines a rank–three D-module. Treating \eta as a large parameter, we then introduce logarithmic derivatives S and T, obtain a Hamilton–Jacobi–type nonlinear system, and construct WKB-type formal solutions. The leading terms of these solutions are governed by algebraic branches of a cubic equation, whose discriminant describes the turning point set, while the differences of the corresponding phase integrals define the Stokes set in the (x_1,x_2)-plane. Passing to the Borel transform in the WKB parameter, we show that the Borel transforms of the Pearcey WKB solutions satisfy a polynomial equation in the Borel variable, and hence are algebraic functions with finitely many branch points. This yields Borel summability and a clear resurgent structure, and makes it possible to interpret Stokes phenomena in terms of discontinuities across branch cuts in the Borel plane. Overall, the Pearcey system provides a concrete prototype for the synthesis of oscillatory integrals, holonomic PDEs, WKB theory, and Borel–Laplace analysis in several variables.

2013于四川大学数学学院基础数学专业获学士学位，2018年于北京大学北京国际数学研究中心获博士学位，2018-2021在清华大学丘成桐数学科学中心做博士后，2021年加入北京雁栖湖应用数学研究院任助理研究员。研究兴趣包括：可积系统，特别是GW理论、LG理论中出现的无穷维可积系统，兴趣在于理解其中的无穷个对称性的代数结构和相关计算。其他兴趣还包括：混合Hodge结构、等单值形变理论、KZ方程。