Speaker: Benjamin Gammage (Harvard University)

Abstract: "Homological" 3d mirror symmetry is an equivalence between the Kapustin-Rozansky-Saulina 2-category and an as-yet-undefined "Fukaya-Fueter" 2-category associated to dual holomorphic symplectic stacks. Many statements, some classical and some new, may be recovered from such an equivalence by decategorification. We will discuss what is known in the toric setting, where decategorification can be used to produce both the Braden-Licata-Proudfoot-Webster hypertoric Koszul duality and a geometric version of Tate's thesis. This is based on joint work with Justin Hilburn & Aaron Mazel-Gee.