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. 

Bio-Sketch:
Yukinobu Toda （戸田 幸伸） is a professor at the Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), the University of Tokyo. He is renowned for his fundamental contributions to algebraic geometry and enumerative geometry, and for bridging the gap between pure mathematics and theoretical physics. He has received several major awards, most notably the 2014 Spring Prize of the Mathematical Society of Japan, one of the most prestigious honors for Japanese mathematicians under the age of 40. He was also an ICM invited speaker in 2014 in Seoul.