# 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_PIRSA:22020061, doi = {10.48660/22020061}, 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}} }

Justin Hilburn Perimeter Institute for Theoretical Physics

## 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