### Mathematics Colloquium

# Heather Lee

### (University of Washington in Seattle)

## "Symplectic geometry and homological mirror symmetry"

** Date: ** |
February 12, 2018 |

** Time: ** |
17:15 |

** Place: ** |
Lecture Hall, Research I |

**Abstract:** Symplectic manifolds are real even-dimensional manifolds that generalize the phase space of classical Hamiltonian mechanical systems of N particles. In a 2N-dimensional symplectic manifold, we can simultaneously have at most N conserved quantities and they determine an N-dimensional submanifold which is an example of a Lagrangian submanifold. Studying Lagrangian submanifolds and how they intersect leads to powerful tools for understanding symplectic geometry and plays a crucial role in explaining mirror symmetry. Mirror symmetry is a remarkable duality between symplectic geometries and complex geometries. We will focus on the homological mirror symmetry (HMS) conjecture, which is a formulation of mirror symmetry. HMS was originally formulated by Kontsevich for mirror pairs of compact Calabi-Yau manifolds. Since then, it has been extended to cover non-Calabi-Yau manifolds and open manifolds as well. This talk will start with a beginner's introduction to symplectic geometry, and it will include the simplest examples as well as recent progress in homological mirror symmetry.

*The colloquium is preceded by tea from 16:45 in the Resnikoff Mathematics Common Room, Research I, 127.*