Categorical Donaldson-Thomas Theory And Dolbeault Geometric Langlands Conjecture
发布时间：2025年10月27日
浏览次数：137
发布者: Ruixin Li
主讲人： Yukinobu Toda (The University of Tokyo)
活动时间： 从 2025-11-04 16:00 到 17:00
场地： 北京国际数学研究中心，镜春园78号院（怀新园）77201室
Abstract:
In this talk, I will give a motivation of my recent work with Tudor Pădurariu (arXiv:2508.19624). I will review Donaldson-Thomas (DT) theory which counts stable coherent sheaves on Calabi-Yau 3-folds, and geometric Langlands correspondence (GLC) proved by Gaitsgory et al in the last year. Then I will explain our proposal relating them; on DT side via categorification and on GLC side via its classical limit. The upshot is a precise formulation of Dolbeault geometric Langlands conjecture by Donagi-Pantev as an equivalence of certain derived categories of moduli stacks of Higgs bundles, where on one side we introduce a new type of categories called `limit category'. I focus on the motivations, and leave mathematical details on my talk on Nov 6.
In this talk, I will give a motivation of my recent work with Tudor Pădurariu (arXiv:2508.19624). I will review Donaldson-Thomas (DT) theory which counts stable coherent sheaves on Calabi-Yau 3-folds, and geometric Langlands correspondence (GLC) proved by Gaitsgory et al in the last year. Then I will explain our proposal relating them; on DT side via categorification and on GLC side via its classical limit. The upshot is a precise formulation of Dolbeault geometric Langlands conjecture by Donagi-Pantev as an equivalence of certain derived categories of moduli stacks of Higgs bundles, where on one side we introduce a new type of categories called `limit category'. I focus on the motivations, and leave mathematical details on my talk on Nov 6.
