The Kapustin-Witten equations and nonabelian Hodge theory
Organizers
Speaker
Time
Tuesday, November 25, 2025 3:00 PM - 4:00 PM
Venue
A7-201
Online
Zoom 388 528 9728
(BIMSA)
Abstract
The moduli spaces of semistable Higgs bundles on a curve have been inspiring lots of researchers across various fields, including Geometry, Topology, Representation Theory, Number Theory, and Mathematical Physics. They have been indeed one of the wealthiest sources, contributing areas of research such as nonabelian Hodge theory, the P=W conjecture, the SYZ style topological Mirror symmetry for the Hitchin fibrations, the Langlands programme and its geometric one, and more. In this talk, I would like to discuss intriguing analogues of them on surfaces, strongly motivated by the Kapustin-Witten and Vafa-Witten theories from topologically twisted versions of N=4 super Yang-Mills one, with a focus on the former in the context of nonabelian Hodge theory. This talk is based partially on joint work with Chih-Chung Liu and Steven Rayan.
Speaker Intro
My research interests are primarily centred on Gauge theory within mathematics. Recently, my focus has been on semistable Higgs sheaves on complex projective surfaces and associated gauge-theoretic invariants, employing algebro-geometric methods. However, I also have a strong interest in working within the analytic category.