Room PK-5115 , Pavillon President-Kennedy, CA
Study of exact Lagrangian submanifolds of a cotangent bundle via sheaf theory.
Let $Lambda$ be a compact exact Lagrangian submanifold of the cotangent bundle of a manifold $M$. The projection to the base gives a homotopy equivalence between $Lambda$ and $M$. This was first proved by Fukaya-Seidel-Smith and Nadler using the Fukaya category. I will explain a more recent proof which relies on the microlocal theory of sheaves. (I will quickly recall the notions of sheaves and microsupport of a sheaf.)