Qingyuan Bai: Revisiting coherent-constructible correspondence for toric variety

Abstract.

From Fulton's beautiful brochure on toric geometry, one can learn about a curious correspondence between ample line bundles on smooth projective toric varieties and integral polytopes in a real vector spaces. I will tell a fairy tale of the categorification of such result, in the context of spectral algebraic geometry - following works of Morelli, Fang-Liu-Treumann-Zaslow and D. Vaintrob. Like many other stories, this one has a joyful ending - where I learn to compute Picard groupoid of sheaves on a real vector space under convolution and get a funny answer.