Manchester Geometry Seminar 1999/2000

In recent years the study of certain highly symmetric quantum theories, known as topological theories, has proved a powerful tool for suggesting new invariants of manifolds. The methodology is from physics, and involves the (usually non-rigorous) manipulation of functional integrals.

The talk will concern a mathematically rigorous treatment of the simplest topological model, the topological particle, including:

• the classical dynamics of the model
• the BRST approach to quantising the model, using ghosts; (at this stage a supermanifold is introduced)
• path integral treatment of the dynamics of the model (here Brownian motion on a manifold and a supermanifold is required)
• the extraction of topological information from the results

(The talk combines elements of several fields, particularly mechanics, probability theory and geometry. Listeners will not need to be experts in any of these fields.)