EVENT DETAILS AND ABSTRACT

Title: Conormal bundles to knots and Large N duality
Speaker: Sergiy Koshkin
Speaker Info: Kansas State University
Brief Description:
Special Note:
Abstract:

Abstract: I will give an introduction to Large N duality between the Chern-Simons theory on the 3-sphere and Gromov-Witten theory on a Calabi-Yau threefold known as the resolved conifold. The duality predicts that to each knot in the 3-sphere there corresponds a Lagrangian submanifold in the resolved conifold and knot invariants such as the HOMFLY polynomial can be recovered from 'open Gromov-Witten invariants' on the other side. Several constructions of such submanifolds were offered but found wanting for one reason or another. I will describe a construction that uses conormal bundles to knots as a starting point and produces submanifolds that are in line with the duality predictions. Then I will talk about geometry of the resolved conifold in relation to open holomorphic curves ending on the constructed submanifolds. In the end I will discuss some open problems concerning the computation of open Gromov-Witten invariants.