Speaker:  Umut Varolgunes (Bogazici University)

Abstract: I will discuss the notion of generalized Delzant subdomains of graded symplectic manifolds and their relative symplectic cohomology. Assuming that we have an involutive decomposition into such domains, I will construct a mirror formal scheme over the Novikov ring. The key is to be able to compute the invariants modulo T^hbar, where hbar is a positive constant depending on the decomposition, finiteness of boundary depth which leads to homology level completeness and an injectivity statement mirror to uniqueness of analytic continuation. Then I will assume the existence of a "homological section" and construct the HMS functor. I will end by discussing when one should expect this functor to be cohomologically full and faithful via the notion of local generation.