Hodge Structures in Symplectic Geometry

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
Video Link:https://video.ias.edu/joint/pantev

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.