PIRSA:25050010

Video URL

https://pirsa.org/25050010

Perverse coherent sheaves and cluster categorifications

Dumanskiy, I. (2025). Perverse coherent sheaves and cluster categorifications. Perimeter Institute for Theoretical Physics. https://pirsa.org/25050010

Dumanskiy, Ilya. Perverse coherent sheaves and cluster categorifications. Perimeter Institute for Theoretical Physics, May. 08, 2025, https://pirsa.org/25050010 

          @misc{ scivideos_PIRSA:25050010,
            doi = {10.48660/25050010},
            url = {https://pirsa.org/25050010},
            author = {Dumanskiy, Ilya},
            keywords = {Mathematical physics},
            language = {en},
            title = {Perverse coherent sheaves and cluster categorifications},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2025},
            month = {may},
            note = {PIRSA:25050010 see, \url{https://scivideos.org/pirsa/25050010}}
          }

Ilya Dumanskiy Massachusetts Institute of Technology (MIT) - Department of Mathematics

Talk numberPIRSA:25050010
DOI10.48660/25050010
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

K-theoretical Coulomb branches are expected to have cluster structure. Cautis and Williams categorified this expectation. In particular, they conjecture (and prove in type A) that the category of perverse coherent sheaves on the affine Grassmannian is a cluster monoidal categorification. We discuss recent progress on this conjecture. In particular, we construct cluster short exact sequences of certain perverse coherent sheaves. We do that by constructing a bridge, relating this (geometric) category to the (algebraic) category of finite dimensional modules over the quantum affine group. This is done by relating both categories to the notion of Feigin--Loktev fusion product.