## Columbia Mathematics Department Colloquium

# Towards a global mirror symmetry

by

# Yongbin Ruan

## University of Michigan

Abstract:

During last twenty years, the mirror symmetry has been a driving force in geometry and physics. Many incredible results have been obtained in mathematics. However, a brief investigation reveals that the current form of mirror symmetry in mathematics is only a "local" form of mirror symmetry concerning about so called large complex structure limit. An interesting problem is if we can gain more information by moving away from large complex structure limit. Namely, is there an interesting theory of "global" mirror symmetry? In this talk, we will cover some of exciting developments in this direction.