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.
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