My research is based on the combination of methods from probability theory and other branches of mathematics, including differential equations and functional analysis, numerical analysis, geometry, and mathematical physics. A current focus is on coupling methods for stochastic processes on continuous state spaces. Here, a common goal is to quantify stability properties and convergence to equilibrium, for example for stochastic differential equations, systems with mean-field interactions, numerical approximations, and both Markov Chain Monte Carlo and sequential Monte Carlo methods. Recently, I am particularly interested in Hamiltonian Monte Carlo methods and (kinetic) Langevin dynamics on high and infinite dimensional state spaces.