Time

Location

Speaker

Abstract

Topology of knots and links in a 3-space is tightly related to combinatorics. This relation was highly promoted by ideas of modern physics leading to so called quantum invariants of knots and links such as the Jones polynomial and others. I am going to show several aspects of this relation.

In the first lecture I will present the classical Thistlethwaite theorem relating the Jones polynomial of a link with the Tutte polynomial of an appropriate planar graph. If time permits, I will describe a generalization of this theorem to virtual links. Here the corresponding graphs turn out to be embedded into higher genus surfaces.

The second lecture will be a brief introduction to the Khovanov homology of links.

Knowledge of a standard courses of linear algebra should be sufficient for understanding at some level. However the familiarity with tensor product of vector spaces and abstract algebra would make it easier.

Notes

This lecture is part of Invitation to Mathematics.
Pre-candidacy students can sign up for this lecture series by registering for one credit hour of Math 693, Call # 21208 (with Prof H. Moscovici).