PIRSA ID: 22020061
Série :
Event Type: Seminar
Domaine(s) scientifique(s) : Mathematical Physics
Date de fin : 2022-02-18
Speaker(s): Justin Hilburn Justin Hilburn
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