CMSA Mathematical Physics Seminar: Coisotropic branes on symplectic tori and homological mirror symmetry
Yingdi Qin - Harvard University
Homological mirror symmetry (HMS) asserts that the Fukaya category of a symplectic manifold is derived equivalent to the category of coherent sheaves on the mirror complex manifold. Without suitable enlargement (split closure) of the Fukaya category, certain objects of it are missing to prevent HMS from being true. Kapustin and Orlov conjecture that coisotropic branes should be included into the Fukaya category from a physics view point. In this talk, I will construct for linear symplectic tori a version of the Fukaya category including coisotropic branes and show that the usual Fukaya category embeds fully faithfully into it. I will also explain the motivation of the construction through the perspective of Homological mirror symmetry.