State Models in Topology, Graph Theory and Statistical Mechanics
Abstract
In this talk the speaker will recount how, in trying to understand John
Horton Conway's skein approach to the Alexander polynomial, he was led to
discover (in 1980) a remarkable state summation model of the Alexander
polynomial, and how this led (in 1984 and 1985) to a state model for the
Jones polynomial and the direct connection of ideas in statistical
mechanics, spin networks and graph theory with the theory of knots and
links in three dimensional space. Subsequently the notion of state sum for
knot and link invariants was generalized to the concept of a topological
quantum field theory and has become a new part of geometric and algebraic
topology in the interface with combinatorics, algebra and mathematical
physics.
R E F R E S H M E N T S
4:00 To 4:25 PM
Kenneth W. Anderson
Memorial Reading Room
