Vivek Shende

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 the 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.  This is joint work with Tobias Ekholm.