|Date:||February 12, 2018|
|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.