PIRSA:22020061

Towards 2-Categorical 3d Abelian Mirror Symmetry: Equivariant Perverse Scobers

APA

Hilburn, J. (2022). Towards 2-Categorical 3d Abelian Mirror Symmetry: Equivariant Perverse Scobers. Perimeter Institute. https://pirsa.org/22020061

MLA

Hilburn, Justin. Towards 2-Categorical 3d Abelian Mirror Symmetry: Equivariant Perverse Scobers. Perimeter Institute, Feb. 18, 2022, https://pirsa.org/22020061

BibTex

          @misc{ pirsa_22020061,
            doi = {},
            url = {https://pirsa.org/22020061},
            author = {Hilburn, Justin},
            keywords = {Mathematical physics},
            language = {en},
            title = {Towards 2-Categorical 3d Abelian Mirror Symmetry: Equivariant Perverse Scobers},
            publisher = {Perimeter Institute},
            year = {2022},
            month = {feb},
            note = {PIRSA:22020061 see, \url{https://pirsa.org}}
          }
          

Abstract

 3d mirror symmetry relates the geometry of dual pairs of algebraic symplectic stack and has served in as

a guiding principle for developments in representation theory. However, due to the lack of definitions, thus far only part of the subject has been mathematically accessible. In this talk, I will explain joint work with Ben Gammage and Aaron Mazel-Gee on formulation of abelian 3d mirror symmetry as an equivalence between a pair of 2-categories constructed from the algebraic and symplectic geometry, respectively, of Gale dual toric cotangent stacks.

In the simplest case, our theorem provides a spectral description of the 2-category of spherical functors -- i.e., perverse schobers on the affine line with singularities at the origin. We expect that our results can be extended from toric cotangent stacks to hypertoric varieties, which would provide a categorification of previous results on Koszul duality for hypertoric categories $\mathcal{O}$.

Zoom Link: https://pitp.zoom.us/j/95205675729?pwd=OXRSTlhiQUxQYm5lLzVLYTE1Z0FLdz09