This school will offer mini-courses designed to rigorously develop important analytic techniques, within the context of certain interesting applications, and illustrate how theory is used in problem solving. The mini-courses will be self-contained, accessible to graduate students, and describe active areas of current research.

Yoshiko Ogata (University of Tokyo)

Hypothesis testing and non-equilibrium statistical mechanics:
This mini-course will focus on connections between non-equilibrium statistical mechanics and quantum information theory, two fields which have seen frequent interplay since Shannon's rediscovery of Gibbs-Boltzmann entropy. The theory of entropic fluctuations and, in particular, results on large deviations for entropy flow will be related to quantum hypothesis testing.

Jeremy Quastel (University of Toronto)

The Kardar-Parisi-Zhang equation and its universality class:
This mini-course will focus on the KPZ equation. It was introduced in 1986 and has become the default model in physics for random interface growth. It is a member of a large universality class with non-standard fluctuations, including directed polymers. Even in one dimension, it turned out to be difficult to interpret and analyze mathematically, but at the same time to have a large degree of exact solvability. The course will survey the history and recent progress.

Benjamin Schlein (Universität Bonn)

Derivation of effective evolution equations from quantum dynamics:
This mini-course will address the problem that fundamental physical evolution equations such as the many-body Schrodinger equation are too complicated to provide useful quantitative information on systems with large numbers of interacting degrees of freedom. The course will describe regimes in which simpler effective evolution equations provide good approximations. Examples are mean field limits and evolution equations for Bose-Einstein condensates.

Simone Warzel (Technische Universität München)

Random Schrödinger operators:
This mini-course will focus on progress in the theory of random Schrödinger operators. A prototype is given by the Anderson model, which provides a rigorous framework in the study of conductivity properties of disordered materials. This will include results for Anderson models on tree graphs, where a more complete understanding of the localization-delocalization transition has recently been obtained.