WKB Asymptotics of Stokes matrices and rhombus inequalities
演讲者
Anton Alekseev
时间
2025年10月10日 13:00 至 14:30
地点
A3-4-301
线上
Zoom 242 742 6089
(BIMSA)
摘要
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
The talk is based on a joint work with A. Neitzke, X. Xu, and Y. Zhou, see https://arxiv.org/abs/2403.17906