Mathematical physics, probability, statistical mechanics, field theories, conformal symmetry, complex analysis, lattice models, exactly solvable models, neural networks.
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.
Stochastic equations, stochastic dynamics, analysis of stochastic processes, stochastic processes on geometric spaces, Multi-scale analysis, Markov processes, rough path theory, analysis on path spaces, Malliavin calculus, numerics of stochastic equations, fluctuation theory of stochastic partial differential equations (SPDES) and singular SPDEs.
Stochastic dynamics, stochastic PDEs, constructive QFT, rough analysis, statistical mechanics.