# Colloquium abstracts

**Christopher Woodward**

Rutgers University, U.S.A.

January 17, 2019

**Mirror symmetry and Lagrangian Floer cohomology**: Mirror symmetry predicts a duality between complex and symplectic geometry. In particular the conjecture relates (in Kontsevich's version) sheaf cohomology of vector bundles with Floer theory of Lagrangian submanifolds. I will discuss some of the ideas behind the conjecture, such as the definition of a Lagrangian submanifold, and some recent work on the mirror analog of deformation of vector bundles which, as suggested by Fukaya-Oh-Ono-Ohta, corresponds to smoothing singularities of the Lagrangians.