Skeins, Clusters and Wavefunctions in Open Gromov-Witten Theory
Explore a cutting-edge lecture on open Gromov-Witten theory and its applications in algebraic topology. Delve into Ekholm and Shende's proposed version, which counts holomorphic maps from Riemann surfaces with boundary landing on a Lagrangian 3-manifold L using the HOMFLYPT skein module. Discover joint research by Gus Schrader, Mingyuan Hu, and Eric Zaslow, presenting a novel method for computing the Ekholm-Shende generating function ('wavefunction') for a specific class of Lagrangian branes in C^3. Examine the innovative use of a skein-theoretic analog of cluster theory, where skein-valued wavefunctions for different Lagrangians are connected through skein mutation operators. Gain insights into this advanced mathematical topic, bridging concepts from algebraic topology, geometry, and quantum field theory.