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Vivek Shende: Lectures

01/09/2020: Skeins on Branes

January 9, 2020
TITLE: Skeins on Branes

ABSTRACT: 30 years ago, Witten explained how the Jones polynomial and its relatives – at the time, the latest word in knot invariants – arise naturally from a certain quantum field theory. Ten years later, Ooguri and Vafa used string theory to argue that the same invariants should count holomorphic curves in a certain Calabi-Yau 3-fold. In this talk, I will explain how to understand their proposal in mathematical terms, and sketch a proof that indeed, the coefficients of the HOMFLY polynomial count holomorphic curves, and, conversely, that the skein relations of knot theory are the key ingredient in defining invariant counts of higher genus holomorphic curves with boundary. This is joint work with Tobias Ekholm.