Mathematical Statistical Mechanics

Statistical mechanics lies at the interface between probability theory and physics. It goes back to the physicists Clausius and in particular Gibbs and Boltzmann. Its aim is to understand the macroscopically observable behavior of materials, in particular so-called phase transitions, on the basis of miscroscopic laws. For example, is it possible to explain how water turns to ice or why materials are magnetic? We will mainly study phase transitions using simple models such as the Ising model, but we will also analyze currently very popular models such as the Gaussian free field. Interestingly, some of the insights gained can also be transferred to non-physical models (e.g. how a memory works).