| Joint IAS-PU Symplectic Geometry Seminar | |
| Topic: | Hodge Structures in Symplectic Geometry |
| Speaker: | Tony Pantev |
| Affiliation: | University of Pennsylvania |
| Date: | Friday, October 21 |
| Time/Room: | 4:30pm - 5:30pm/S-101 |
I will explain how essential information about the structure of symplectic manifolds is captured by algebraic data, and specifically by the non-commutative (mixed) Hodge structure on the cohomology of the Fukaya category. I will discuss how mirror symmetry leads to Hodge theoretic symplectic invariants arising from twist functors, and from geometric extensions. I will also explain how the instanton-corrected Chern-Simons theory fits in the framework of normal functions in non-commutative Hodge theory and will give applications to explicit descriptions of quantum Lagrangian branes. This is a joint work with L. Katzarkov and M. Kontsevich.