Seminar in Real and Complex Geometry

Thursday, December 5, 2024, 16:15-17:45, online via zoom




Gus Schrader
(Northwestern University

Skeins, clusters and wavefunctions


Abstract
             

Ekholm and Shende have proposed a version of open Gromov-Witten theory in which holomorphic maps from Riemann surfaces with boundary landing on a Lagrangian 3-manifold L are counted via the image of the boundary in the HOMFLYPT skein module of L. I'll describe joint work with Mingyuan Hu and Eric Zaslow which gives a method to compute the Ekholm-Shende generating function ('wavefunction') enumerating such maps for a class of Lagrangian branes L in C^3. The method uses a skein-theoretic analog of cluster theory, in which skein-valued wavefunctions for different Lagrangians are related by skein mutation operators.