PIRSA:25050010

Perverse coherent sheaves and cluster categorifications

APA

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

MLA

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

BibTex

          @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/index.php/pirsa/25050010}}
          }
          

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

Talk numberPIRSA:25050010
Source RepositoryPIRSA

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.