报告题目: Resurgent Asymptotics: Error Bounds, WKB Analysis, and the Stokes Phenomenon

报 告 人：Gergő Nemes 教授（哈尔滨工业大学）

报告时间：2026年9月3日（周四）上午10：00—11：00

报告地点: 广东工业大学龙洞校区行政楼610

报告摘要: Divergent asymptotic expansions naturally arise across pure and applied mathematics, quantum mechanics, and mathematical physics. While classical asymptotic analysis provides useful approximations, resurgent analysis reveals the rich structures hidden within divergent series. In this talk, I will present an overview of my research over the past decade on exact asymptotics, resurgence theory, and applications of these ideas. First, I will discuss the development of global, explicit, and computable error bounds for asymptotic expansions of contour integrals, special functions (such as Airy and Legendre functions), and implicit functions, complementing and extending the classical differential equation approach of Frank W. J. Olver. Second, I will discuss formal WKB solutions of higher-order linear differential equations and their Borel summability. Third, I will address the Stokes phenomenon and its higher-order manifestations, including Berry’s smoothing of Stokes transitions and Howls' hyperterminant conjecture. Finally, I will outline my ongoing and future research vision, focusing on exact resurgence in exact WKB analysis, Borel summability for general higher-order linear differential equations, and spectral problems.

报告人简介: Gergő Nemes is a Professor in the School of Mathematics at the Harbin Institute of Technology, China. He obtained a B.Sc. in mathematics (with distinction) and a M.Sc. in mathematics (with honours) from Loránd Eötvös University, Budapest, Hungary and a Ph.D. in mathematics from Central European University in Budapest, Hungary. Nemes has research interests in asymptotic analysis, Écalle theory, exact WKB analysis, and special functions.