Tel-Aviv University
School of Mathematical Sciences

Department Colloquium

Monday, October 22, 2012

Schreiber 006, 12:15

Michael Polyak


Knot and 3-manifold invariants via counting graphs and surfaces

I will start with a short overview of the so-called perturbative invariants of links and 3-manifolds.
While these invariants were intensively studied in the last two decades, many questions, inconsistencies
and problems persist. The reason is that the construction is based on some complicated Feynman integrals
in the perturbative Chern-Simons theory and a lot of technicalities are involved. In the main part of the talk I
will describe an alternative elementary combinatorial construction of these invariants. It involves counting
similar trivalent graphs in a link diagram. This approach immediately extends to invariants of 3-manifolds.
Our construction can be restated in terms of counting certain surfaces ending on a link diagram. The latter
description seem to be a combinatorial counterpart of a so-called "large N duality conjecture" by
Gupakomar-Vafa, relating  Chern-Simons theory to open strings.

Coffee will be served at 12:00 before the lecture
at Schreiber building 006