Algebraic Geometry Seminar: David Treumann

Abstract:

The coherent constructible correspondence matches coherent sheaves on a toric variety to constructible sheaves on a compact torus T^n. Microlocal sheaf theory allows one to view the latter sort of object as a Lagrangian submanifold in the symplectic manifold T^n x R^n, making this a form of mirror symmetry. I will discuss this correspondence, and an extension of of it to hypersurfaces in toric varieties, which in some sense matches coherent sheaves to Legendrian submanifolds of the contact manifold T^n x S^{n-1}.