报告人：Laura Fredrickson（俄勒冈大学）
时间：2026年4月15日10:30-11:30
地点：腾讯会议：254 230 427，无需密码
Hitchin's equations are a system of gauge theoretic equations on a Riemann surface that are of interest in many areas including representation theory, Teichm\"uller theory, and the geometric Langlands correspondence. The Hitchin moduli space carries a natural hyperk\"ahler metric, a rich and rigid geometric structure. An intricate conjectural description of its asymptotic structure appears in the work of Gaiotto--Moore—Neitzke. In recent years, a number of mathematicians have proved aspects of this conjecture using tools from geometric analysis. Many results comparing Hitchin's hyperkahler metric to the *semiflat hyperkahler metric* on smooth fibers now exist. More recently, mathematicians have begun to study the behavior of Hitchin's hyperkahler metric *near singular fibers* of the Hitchin fibration; keywords here are "Hitchin's subintegrable system" and "Ooguri-Vafa geometries".
In this talk I will focus on Gaiotto-Moore-Neitzke's conjecture near the singular fibers. I will motivate Gaiotto-Moore-Neitzke's conjecture via Gross-Wilson's classic result about K3 metrics near their large complex structure limit. Then, I will explain Gaiotto-Moore-Neitzke's formalism and state their conjecture, relating it to Hitchin moduli spaces. Then, I will discuss the picture of the metric behavior near singular fibers, describing Ooguri-Vafa model metrics in detail. This talk will focus on joint work in 2501.01675 with Max Zimet.
