Tobias Ekholm: Knot contact homology, Chern-Simons, and topological strings

Abstract

We discuss recent developments relating contact geometry in dimension 5 to physically inspired topology in dimension 3.  A brief description is as follows:
  In 1989 Witten explained the Jones and HOMFLY polynomials of knot theory in terms of Chern-Simons theory gauge theory in dimension 3. In 1992 he further showed that Chern-Simons theory of a 3-manifold is equivalent to an open topological string theory in its cotangent bundle. In 1999 Ooguri-Vafa reinterpreted this open string theory for the 3-sphere as a closed string theory in the resolved conifold X, or, in mathematical language, the Gromov-Witten theory of X that counts holomorphic curves. They similarly gave curve counting interpretations of the HOMFLY polynomial. In 2014 Aganagic, Ekholm, Ng, and Vafa related the counts of the simplest curves, the disks, for the HOMFLY to knot contact homology, which is a Floer homological theory in the unit cotangent bundle of the 3-sphere and which can be combinatorially computed. This gives a new effective way of approaching the theories discussed above from infinity. Work in progress gives similar descriptions of curve counts at arbitrary genus through a more elaborate theory at infinity.
  The talk will survey these developments and will be accessible to a general mathematical audience.

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Tobias Ekholm: Knot contact homology, Chern-Simons, and topological strings (audio only, mp3)

Tobias Ekholm: Knot contact homology, Chern-Simons, and topological strings (audio and video, mp4)

Kollokvier 2016

Titel Datum
Karen Smith 2016‑12‑07
Jeff Steif: Noise Sensitivity of Boolean Functions and Critical Percolation 2016‑10‑28
Martin Hairer: Taming infinities. 2016‑09‑29
Mattias Jonsson: Complex, tropical and non-Archimedean geometry 2016‑06‑01
Yulij Ilyashenko: Towards the global bifurcation theory on the plane 2016‑04‑27
Volodymyr Mazorchuk: (Higher) representation theory 2016‑03‑09
Tobias Ekholm: Knot contact homology, Chern-Simons, and topological strings 2016‑02‑10