Lagrangian Floer Homology and Mirror Symmetry

Speaker: 
Kenji Fukaya
Date: 
Tue, Jul 7, 2009
Location: 
University of New South Wales, Sydney, Australia
Conference: 
1st PRIMA Congress
Abstract: 
This is a survey of Lagrangian Floer homology which I developed together with Y.G.-Oh, Hiroshi Ohta, and Kaoru Ono. I will focus on its relation to (homological) mirror symmetry. The topic discussed include
  1. Definition of filtered A infinity algebra associated to a Lagrangian submanifold and its categorification.
  2. Its family version and how it is related to mirror symmetry.
  3. Some example including toric manifold. Calculation in that case and how mirror symmetry is observed from calculation.