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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 > Topics in Representation Theory WKB Asymptotics of Stokes matrices and rhombus inequalities
WKB Asymptotics of Stokes matrices and rhombus inequalities
Organizers
Semen Artamonov , Yevgen Makedonskyi , Pavel Nikitin , Shamil Shakirov
Speaker
Anton Alekseev
Time
Friday, October 10, 2025 1:00 PM - 2:30 PM
Venue
A3-4-301
Online
Zoom 242 742 6089 (BIMSA)
Abstract
Stokes matrices of first order ODEs are conjectured to have WKB type asymptotics with respect to the small parameter in front of the derivative term. For the simple case of a rank n system on P^1 with a simple pole at zero and a double pole at infinity, the Boalch Theorem in Poisson Geometry implies an interesting system of rhombus inequalities on leading WKB exponents. For very large values of the coefficient in front of the double pole (the caterpillar line), these inequalities reduce to Cauchy interlacing inequalities. We show that near the caterpillar line one can relate these inequalities to positivity of certain periods on the spectral curve of the system. Our analysis relies on the Gaiotto-Moore-Neitzke spectral network theory which makes predictions for WKB asymptotics in terms of the data of the spectral curve.

The talk is based on a joint work with A. Neitzke, X. Xu, and Y. Zhou, see https://arxiv.org/abs/2403.17906
Beijing Institute of Mathematical Sciences and Applications
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