Talk page
Title:
Mirror construction using non-commutative geometry
Speaker:
Abstract:
Strominger-Yau-Zaslow proposed that the mirror of a Kaehler manifold can be constructed from deformations of fibers of a Lagrangian torus fibration. In this talk we develop a construction which is related but different from SYZ. Namely we consider a deformation space of a set of Lagrangian submanifolds which are not necessarily tori. We will see that this space is naturally non-commutative in nature. Moreover it can be regarded as a “mirror” in a generalized sense, namely there exists a natural functor from the Fukaya category to the category of modules over this space. The functor always carries a certain injectivity property. The construction is particularly useful for systems in which collections of Lagrangians are canonically constructed. Calabi-Yau threefolds associated to Hitchin systems over Riemann surfaces provide a beautiful class of examples. This is a joint work with Cheol-Hyun Cho and Hansol Hong.
Link:
Workshop: