SAG: Topology of Galois conjugate character varietiesSeminar Algebraic Geometry (SAG)

by Siqing Zhang (MPI)

Thursday Oct 29, 2026, 10:30 AM → 11:30 AM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

How subtle can the difference between two Galois conjugate complex varieties be? Can they have isomorphic homotopy groups and rational cohomology rings, but nonisomorphic integral cohomology rings? In joint work with Junliang Shen, we show that the answer is yes and the example arises naturally as certain character varieties for curves, answering a 2005 question of Hausel. The proof uses non abelian Hodge theory and develops a systematic method for finding the lowest-degree relation among tautological classes in the cohomology of Higgs moduli spaces, a problem that had previously remained mysterious beyond rank two.