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About
President
Governance
Partner Institutions
Visit
People
Management
Faculty
Postdocs
Visiting Scholars
Administration
Academic Support
Research
Research Groups
Courses
Seminars
Join Us
Faculty
Postdocs
Students
Events
Conferences
Workshops
Forum
Life @ BIMSA
Accommodation
Transportation
Facilities
Tour
News
News
Announcement
Downloads
Qiuzhen College, Tsinghua University
Yau Mathematical Sciences Center, Tsinghua University (YMSC)
Tsinghua Sanya International  Mathematics Forum (TSIMF)
Shanghai Institute for Mathematics and  Interdisciplinary Sciences (SIMIS)
BIMSA > WKB analysis and hypergeometric differential equation Exact WKB for Second-order linear ODEs
Exact WKB for Second-order linear ODEs
Organizers
Yong Li , Xinxing Tang , Luyao Wang
Speaker
Luyao Wang
Time
Saturday, October 18, 2025 2:00 PM - 4:00 PM
Venue
A3-3-301
Online
Zoom 442 374 5045 (BIMSA)
Abstract
WKB approximation is a technique for finding approximate solutions to linear differential equations with spatially varying coefficients. It is typically used for a semiclassical calculation in quantum mechanics. In this talk, I will discus the exact WKB analysis for second-order linear ordinary differential equations. Starting from the classical WKB approximation, we derive formal solutions whose coefficients grow factorially and therefore form Gevrey-1 series. We then review the Borel transform, Borel summation, and Watson's lemma, which together assign analytic meaning to these divergent series. Under suitable, non-degenerate Stokes geometry, WKB series are Borel summable in each Stokes region and their Borel sums provide genuine analytic solutions. We describe the global Stokes picture, Voros connection formulae across Stokes curves, and the normalization at turning points and regular singular points. Finally, we show how the Borel-resummed WKB solutions yield monodromy matrices for second-order Fuchsian equations by transporting solutions along closed contours and multiplying the local connection data. This talk refers to Takashi Aoki's lecture notes.
Beijing Institute of Mathematical Sciences and Applications
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