Mirror Symmetry via Floer Theoretic Invariants

Explore mirror symmetry through Floer theoretic invariants in this advanced mathematics lecture. Delve into the concept of generalized Delzant subdomains of graded symplectic manifolds and their relative symplectic cohomology. Learn how to construct a mirror formal scheme over the Novikov ring, assuming an involutive decomposition into such domains. Discover the key techniques for computing invariants modulo T^hbar, where hbar is a positive constant dependent on the decomposition. Examine the finiteness of boundary depth leading to homology level completeness and an injectivity statement mirror to uniqueness of analytic continuation. Investigate the construction of the HMS functor under the assumption of a "homological section" existence. Conclude by discussing the conditions under which this functor is expected to be cohomologically full and faithful, utilizing the notion of local generation.