Numerical invariants from bounding chains

Homological Mirror Symmetry (minicourse)
Topic:Numerical invariants from bounding chains
Speaker:Jake Solomon
Affiliation:Hebrew University of Jerusalem; Visitor, School of Mathematics
Date:Wednesday, December 14
Time/Room:10:45am - 12:00pm/S-101
Video Link:https://video.ias.edu/homomirrorsym/2016/1214-JakeSolomon

I'll begin with a leisurely introduction to Fukaya A-infinity algebras and their bounding chains. Then I'll explain how to use bounding chains to define open Gromov-Witten invariants. The bounding chain invariants can be computed using an open analog of the WDVV equations. This leads to an explicit understanding of the homotopy type of certain Fukaya A-infinity algebras. Also, the bounding chain invariants generalize Welschinger's real enumerative invariants. A nice example is real projective space considered as a Lagrangian submanifold of complex projective space. This is joint work with Sara Tukachinsky.