Interests and Projects
My research is focused on Dynamical Systems and its relations to Probability, Analysis and Geometry. FirstIy, I am working on problems in random dynamical systems, in particular (chaotic) random attractors and their parameter-dependent change (bifurcations). Furthermore, I am investigating multiscale systems with non-hyperbolic singularities, analyzing discretization problems for ODEs, SDEs and PDEs. Additionally, I am working on models of stochastic dynamics in applications, with an increased focus on chemical reaction, learning and atmospheric dynamics.
Keywords: Fast-slow systems, stochastic and random differential equations, smooth ergodic theory, random attractors, bifurcation theory, diffusion with absorption at the boundary, population dynamics, jump processes, reaction-diffusion systems.
Projects as Principal Investigator :
Funded by Deutsche Forschungsgemeinschaft (DFG)
MATH+ AA1-18: Synchronization and Geometric Structures of Stochastic Biochemical Oscillators
MATH+ AA1-8: Random Bifurcations in Chemical Reaction Networks
SPP 2298: Multiscale Dynamics of Neural Nets via Stochastic Graphops
CRC 1114: Characterization and Prediction of Quasi-stationary Atmospheric States
Funded by Einstein Foundation Berlin