This website uses features that are not well-supported by your browser. Please consider upgrading to a browser and version that fully supports CSS Grid and the CSS Flexible Box Layout Module.
Sidebar image
NB: A PDF version of this announcement (suitable for posting) is also available.

Skeins and Characters

Charles Frohman
The University of Iowa

Thursday, February 2, 2012
008 Kemeny Hall, 4 pm
Tea 3:30 pm, 300 Kemeny Hall

Abstract: The Kauffman bracket skein relation is a linear relation between knot diagrams that differ at a single crossing. It can be used to compute the Jones polynomial effectively. I will explain the relationship between the Kauffman bracket skein relation and the Cayley-Hamilton identity for $2\times 2$ matrices of determinant $1$. This leads to defining algebras from knot diagrams on surfaces that are deformations of character rings of surface groups. I will then give a geometric explanation of the Jones polynomial in terms of character varieties of surface groups.\par The first 30 minutes of the talk should be accessible to advanced undergraduates, the next 20 will require some acquaintance with algebraic and symplectic geometry

This talk will be accessible to undergraduate students.