Mini-Workshop: Recent Progress in Path Integration on Graphs and Manifolds

Abstract

Ever since Richard Feynman's PhD thesis, path integrals have played a decisive role in mathematical physics. While it is well-known that such formulae can hold only formally, it was Mark Kac who realized that by replacing the unitary group by the heat semigroup, one obtains well-defined and rigorous formulae. Following this pioneering work, Feynman-Kac path integral formulae have been adapted to several situations and generalized into several directions providing the central focus of this workshop.