Special Colloquium
David Treumann
Northwestern
Mirror symmetry and constructible sheaves
Abstract: I will give an introduction to the "microlocal" theory of
constructible sheaves in the sense of Kashiwara and Schapira, and
discuss some recent applications of this theory to Kontsevich's
homological mirror symmetry (HMS) conjectures. HMS seeks to relate
symplectic geometric objects (such as Lagrangian submanifolds)
attached to a symplectic manifold X to complex geometric objects (such
as holomorphic vector bundles) attached to a complex manifold Y. The
symplectic objects can be described in microlocal terms when X is a
cotangent bundle; the cotangent bundle of a compact torus is
especially relevant for mirror symmetry. I will discuss the
"coherent-constructible correspondence" which matches these objects to
coherent sheaves on toric varieties, and an extension of this
correspondence to hypersurfaces.
Monday January 9, 2012 at 3:00 PM in SEO 636