Mathematical physics by analytical methods, specifically spectral theory of ergodic Schrödinger operators and random matrices; homogenization theory; quantum spin systems; matrix inequalities and quantum information theory
Probability theory, Stochastic Processes, Stochastic Analysis, Stochastic Partial Differential Equations, Stochastic Control.
Brownian Sheet – Brownian Motion.
Study of random curves, surfaces and other random geometric structures, that help to geometrically encode and describe the large-scale behaviour of complex systems like, for example, 2D statistical physics models.
Development of statistical methodology, investigation of probability models and analysis of data that arise in natural sciences.