Tropical disk counts

10/19/2021 8:30 pm - 9:30 pm

Abstract: (joint with S. Venugopalan)  I will describe version of the Fukaya algebra that appears in a tropical degeneration with the Lagrangian being one of the “tropical fibers”. An example is the count of “twenty-one disks in the cubic surface” (suggested by Sheridan)  which is an open analog of the twenty-seven lines.  As an application, I will explain why the Floer cohomology of such tropical fibers is well-defined; this is a generalization fo a result of Fukaya-Oh-Ohta-Ono for toric varieties.