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GRASP seminar
GRASP seminar
Categorical Donaldson–Thomas theory and the Dolbeault geometric Langlands conjecture
Categorical Donaldson–Thomas theory and the Dolbeault geometric Langlands conjecture
Organizers
Pengfei Huang
,
Tao Su
, Hao Sun
,
Mengxue Yang
Speaker
Yukinobu Toda
Time
Wednesday, October 28, 2026 2:30 PM - 4:00 PM
Venue
A7-101
Online
Zoom 230 432 7880
(BIMSA)
Abstract
In this talk, I will explain how categorical Donaldson–Thomas (DT) theory leads to a new formulation of the Dolbeault geometric Langlands conjecture proposed by Donagi–Pantev as a classical limit of the de Rham geometric Langlands correspondence. The key ingredient is the notion of limit categories associated with moduli stacks of Higgs bundles, which may be viewed as classical limits of categories of D-modules on moduli stacks of bundles over curves. Our formulation predicts an equivalence between the derived categories of moduli stacks of semistable Higgs bundles and the limit categories associated with moduli stacks of all Higgs bundles on the Langlands dual side. I will explain some fundamental properties of limit categories, including compact generation, Hecke operators, and semiorthogonal decompositions into quasi-BPS categories, which categorify BPS invariants in DT theory. This is based on joint work with Tudor Pădurariu (arXiv:2508.19624).