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GRASP seminar
GRASP seminar
The Dolbeault geometric Langlands conjecture for type A groups beyond the elliptic locus
The Dolbeault geometric Langlands conjecture for type A groups beyond the elliptic locus
Organizers
Pengfei Huang
,
Tao Su
, Hao Sun
,
Mengxue Yang
Speaker
Yukinobu Toda
Time
Wednesday, November 4, 2026 2:30 PM - 4:00 PM
Venue
A7-101
Online
Zoom 230 432 7880
(BIMSA)
Abstract
In this talk, I will discuss a proof of the Dolbeault geometric Langlands conjecture for $\text{GL}_r$ and the Langlands dual pair $\text{SL}_r/\text{PGL}_r$ over an open locus of the Hitchin base which strictly contains the elliptic locus. This open locus includes spectral curves with at worst type A singularities, without any restriction on the number of irreducible components. The conjecture is formulated using limit categories, introduced in joint work with Tudor Pădurariu, and predicts an equivalence between derived categories of moduli stacks of semistable Higgs bundles and limit categories associated with moduli stacks of all Higgs bundles. Beyond the elliptic locus, the latter stacks are not quasi-compact and contain infinitely many Harder–Narasimhan strata, making the use of limit categories essential. I will explain the main ideas of the proof, including the Whittaker normalization conjecture, which plays a key role in establishing the equivalence. This talk is based on arXiv:2606.28878.