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 $\mathcal{O}$.