黄鹏飞 , 苏桃 , 孙浩 , 杨梦雪

Yukinobu Toda

2026年11月04日 14:30 至 16:00

A7-101

Zoom 230 432 7880 (BIMSA)

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.