Research

• under construction -

Research outline

I am both a fundamental scientist and an ethics scholar, with relevant domain expertise in mathematics, artificial intelligence, climate modelling and ethics of technology. I investigate machine learning algorithms, evaluate their reliability and explainability, and draw attention to the ethical implications of our usage of this technology. I do fundamental research on large-scale geophysical flows and created a model to monitor CO2 emissions on a regional scale, which is important for policy decisions. My mathematical models appear as key working mechanisms from epidemiology, neurophysiology, to material sciences.

Having studied philosophy and theology, I know a diverse set of methodologies from the humanities and social sciences, which I applied in the last two years in interdisciplinary research in digital humanities (applied on 2000 year old papyrical manuscripts), and social sciences (gender studies, social migration).

Some words on my pure mathematics topics

Interacting Particle Systems

Interacting particle systems model complex phenomena in natural and social sciences. These phenomena involve a large number of interrelated components, which are modeled as particles confined to a lattice. I study so-called interacting diffusion models, i.e. I consider continuous on-site variables. Therefore my models take the form of a system of coupled stochastic differential equations. My goal is to describe the macroscopic behavior of the interacting diffusion as a nonlinear stochastic partial differential equation.

Gradient flows of non-convex potentials

Gradient flows describe the evolution of a system as the steepest descent of an energy potential. This means that our system is minimizing its energy over time. Non-convex potentials, appearing for example in phase transitions or image processing, give rise to forward-backward parabolic PDEs. I try to determine the regime of initial data under which we can prove existence of solutions to such PDEs. Moreover, I study the behavior and properties of solutions to forward-backward parabolic PDEs.

Methods of Statistical Mechanics in Turbulence

A very prominent feature of turbulent flows, which appear in fluid dynamics, meteorology and engineering (e.g. in combustion phenomena), is the spontaneous appearance of large-scale, long-lived vortices, e.g. Jupiter's Great Red Spot. Though the distributions of vorticity in the actual flow of normal fluids are continuous, in many cases a set of discrete vortices provides a reasonable approximation. I study these point vortex models with methods of statistical mechanics.