Alice Rogers (King's College, London)
alice.rogers@kcl.ac.uk
First I shall briefly describe a generalisation of Brownian motion to paths in anticommuting space.
Next supermanifolds built by adding anticommuting directions to conventional manifolds will be described, and it will be shown how this allows geometric operators such as the Hodge-de Rham operator and the Dirac operator to be represented as differential operators.
Combining these two things makes possible a rigorous version of the fermionic path integrals used in quantum physics to study a number of geometric Laplacians. Examples will be given of this in action.