Knot Invariants in Relation to Statistical Mechanics and Quantum Field Theory

Abstract: This talk will explain a construction due to the speaker (the bracket polynomial) that is a state summation model for the Jones polynomial. This state summation is part of a larger structure that includes the Potts model in statistical mechanics and it has a quantum field theoretic interpretation via the functional integral approach of Edward Witten. We will explain the basics of these relationships without any prior knowledge required of these areas of mathematics and physics.

mathematical physicsalgebraic topology

Audience: advanced learners

Göttingen Colloquium of the Research Traininig Group "Fourier Analysis and Spectral Theory"