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You-Cheng Chou ( Korea Institute for Advanced Study ) 
2026-04-27  10:50 - 11:50
Room 202, Astronomy and Mathematics Building

In this talk, I will first review the literature on the finite-gap KdV hierarchy and the classical Lamé equation to motivate our study. Building on this, this talk introduces a new geometric framework for studying the generalized Lamé equation. We outline the construction of generalized Lamé curves and their relation with the generalized Hermite-Halphen ansatz. A key result presented is a degeneration theorem for the collision of singular points. This theorem allows us to construct a flat family of generalized Lamé curves, making it possible to study the underlying geometry inductively. Finally, we demonstrate how the techniques developed for this theorem solve and generalize Treibich's recent conjecture concerning the enumeration of finite-gap potential to the KdV hierarchy.

This is the joint work with Chin-Lung Wang, and Po-Sheng Wu. This talk is the first in a series; a second talk, to be given by Po-Sheng Wu, will discuss further applications.