In World Mathematical Year 2000 the traditional St. Flour Summer School
was hosted jointly with the European Mathematical Society. Sergio
Albeverio reviews the theory of Dirichlet forms, and gives applications
including partial differential equations, stochastic dynamics of quantum
systems, quantum fields and the geometry of loop spaces. The second
text, by Walter Schachermayer, is an introduction to the basic concepts
of mathematical finance, including the Bachelier and Black-Scholes
models. The fundamental theorem of asset pricing is discussed in detail.
Finally Michel Talagrand, gives an overview of the mean field models for
spin glasses. This text is a major contribution towards the proof of
certain results from physics, and includes a discussion of the
Sherrington-Kirkpatrick and the p-spin interaction models.