### Areas of Research

Irregular phenomena play a role in almost all fields of natural science and technology, and increasingly in the social sciences. One is often dealing with systems which evolve erratically under the influence of random perturbations, or because of their intrinsic complexity.

We list some of the pertinent fields of research and its applications under study at BiBoS

- Mathematics: Dynamical Systems. Probability Theory: stochastic analysis, infinite dimensional diffusions, (infinite dimensional) stochastic differential equations, stochastic partial differential equations, mathematical statistical mechanics, random fields, Markov processes/fields, analysis on Wiener space, measure-valued diffusions. Potential Theory: Dirichlet forms, capacities, axiomatics. Partial Differential Equations: elliptic and parabolic regularity. Spectral Theory.
- Physics: Statistical Mechanics, Quantum (Field) Theory.
- Biology: Epidemiology.
- Sociology: Multi-Agent Models.
- Economics: Stochastic models for financial markets, spatial economic models, equilibria with random agents, evolutionary game theory.