Groechenig-Wyss-Ziegler's proof of the Hausel-Thaddeus conjecture I

BIMSA-YMSC Number Theory Lunch Seminar

Organizers：

Yong Suk Moon, Koji Shimizu

Speaker：

Yuuji Tanaka（BIMSA）

Time：

Thur., 12:00-13:00, Mar. 19, 2026

Venue：

BIMSA A4-1

Title：

Groechenig-Wyss-Ziegler's proof of the Hausel-Thaddeus conjecture I

Abstract:

I'll present an overview of the proof by Groechenig–Wyss–Ziegler of the Hausel–Thaddeus conjecture on a form of topological mirror symmetry between the moduli spaces of semistable Higgs bundles for the groups SL_n and PGL_n. After reviewing the background of mirror symmetry and the geometry of Higgs bundle moduli spaces, especially the Hitchin fibration and duality of generic fibers, I will outline how their argument reduces the conjecture to an arithmetic comparison of (stringy) Hodge numbers. Their key idea is to translate the equality of stringy E-polynomials into a comparison of point counts over finite fields, and to prove this equality using p-adic integration on the moduli stacks.