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Seminar

22.09.2025   at 15:00 - 16:00

QM Research Seminar: Skein Valued Cluster Theory and Open Gromov-Witten Invariants

For a Lagrangian&nbsp;submanifold living in Calabi-Yau threefold, Ekholm and Shende defined a wavefunction living in the HOMFLY-PT skein module of the Lagrangian, which encode open Gromov-Witten invariants in all genus&nbsp;and arbitrarily many boundary components. We develop a skein valued cluster theory to compute these wavefunctions for a class of Lagrangians&nbsp;in $\bC^3$. &nbsp;Along the way we define a skein dilogarithm and prove a pentagon relation. We will also consider the Agangaic-Vafa brane in a class of toric&nbsp;Calabi-Yau threefolds. Part of this talk is based on joint works with Schrader, Zaslow&nbsp;and Shende.<br>

For a Lagrangian submanifold living in Calabi-Yau threefold, Ekholm and Shende defined a wavefunction living in the HOMFLY-PT skein module of the Lagrangian, which encode open Gromov-Witten invariants in all genus and arbitrarily many boundary components. We develop a skein valued cluster theory to compute these wavefunctions for a class of Lagrangians in $\bC^3$.  Along the way we define a skein dilogarithm and prove a pentagon relation. We will also consider the Agangaic-Vafa brane in a class of toric Calabi-Yau threefolds. Part of this talk is based on joint works with Schrader, Zaslow and Shende.
22 Sep