Abstract:Let M be a symplectic manifold and L be a Lagrangian submanifold. Celebrated work of Fukaya-Oh-Ohta-Ono constructs a filtered cyclic A-infinity algebra structure on the cochain (cohomology) group of L by studying moduli spaces of pseudo-holomorphic disks to (M,L) with boundary mark points. In this talk, I will explain how this A-infinity algebra lifts to the free loop space of L in a ...
AbstractThe study of moduli spaces of hyperKahler manifolds and low dimensional cubic hypersurfaces is an active direction in algebraic geometry. Thanks to kinds of Torelli theorem, many moduli spaces can be realized as locally symmetric varieties of unitary type or orthogonal type. Hodge theory, birational geometry and arithmetic geometry converge in this topic. In this talk I will give a gene...