Lectures on Probability Theory and Statistics

Sergio Albeverio: Theory of Dirichlet forms and applications. - Functional analytic background: semigroups, generators, resolvents. - Closed symmetric coercive forms associated with Co-contraction semigroups. - Contraction properties of forms, positivity preserving and submarkovian semigroups. - Potential Theory and Markov Processes associated with Dirichlet Forms. - Diffusions and stochastic differential equations associated with classical Dirichlet forms. - Applications. - Walter Schachermayer: Introduction to the Mathematics of Financial Markets. - Introduction: Bachelier s Thesis from 1900. - Models of Financial Markets on Finite Probability Spaces. - The Binomial Model, Bachelier s Model and the Black-Scholes Model. - The No-Arbitrage Theory for General Processes. - Some Applications of the Fundamental Theorem of Asset Pricing. - Michel Talagrand: Mean field models for spin glasses: a first course. - What this is all about: the REM. - The Sherrington-Kirkpatrick model at high temperature. - The p-spin interaction model. - External field and the replica-symmetric solution. - Exponential inequalities. - Central limit theorems and the Almeida-Thouless line. - Emergence and separation of the lumps in the p-spin interaction model.