Geometry/Physics Seminar

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

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.

Date: Friday, February 10, 2006
Time: 3:00pm
Where: Lunt 101
Contact Person: Prof. Chiu-Chu Melissa Liu
Contact email: ccliu@math.northwestern.edu
Contact Phone: 847-467-1874
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