Algebra / Topology Seminar

Speaker: Vivek Shende

Title: Skeins on branes

Abstract: The HOMFLYPT polynomial is a knot invariant defined in terms of a knot diagram by some elementary "skein relations" which historically originate in quantum topology. However both the relations and the invariant have been lacking a rigorous geometric 3-dimensional (in terms of the knot in the 3-sphere rather than the diagram on the page) interpretation. In the talk I will explain a rigorous geometric 6-dimensional (in terms of the cotangent bundle) interpretation of both the relations and the invariant, and in particular prove the Ooguri-Vafa conjecture -- the HOMFLYPT polynomial of a knot is a count of holomorphic curves in the resolved conifold. This talk presents joint work with Tobias Ekholm.