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“Knot contact homology,
Chern-Simons, and topological strings “
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Date:
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Download-files:
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Time:
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Wednesday, 10. Feb. 2016
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Audio-only-Recording as MP3-File
(smallest possible size):
- Audio.mp3 (ca.30 Mb)
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Video-Recording for any system with MP4-support:
- Video.mp4 (ca.270 Mb)
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15:15 – 16:20
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Speaker :
Tobias Ekholm (Uppsala
Universitet)
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.