Derived & Noncommutative Geometry: Tame Defects and Parahoric Hitchin Systems

Speaker: Lutian Zhao (Kavli IPMU)

Time: 2026-02-23 15:00-18:00
Location: R1110,SIMIS

Abstract:

Motivated by the gauge-theoretic picture of surface defects / tame ramification (Gukov-Witten) and its reincarnations in class S and defect constructions (e.g. Chacaltana-Distler-Tachikawa), I will discuss two related projects around ramified Hitchin systems. First, I will review my joint work with Kydonakis on D-level structures on parahoric torsors and the resulting logahoric/parahoric Hitchin moduli, where a natural moment-map description produces Poisson moduli spaces whose Hitchin maps are algebraically completely integrable Hamiltonian systems. Second, I will explain how residually nilpotent (tame nilpotent-residue) Higgs bundles arise as a special regime of this level-structured setup. Here the abelianization data must reflect jumping Weyl symmetry near marked points (local stabilizers given by reflection subgroups attached to the nilpotent type), leading to a cameral/spectral description compatible with these residue constraints. The final goal is to explain topological mirror symmetry of residually nilpotent Higgs bundles.