Welcome

to my website. I am a mathematician working in the area of probability theory and stochastic analysis. Currently I am a PostDoc with Prof. Dr. Peter Friz at TU Berlin.

Previously, I was a PostDoc in the groups of Prof. Dr. Michael Röckner in Bielefeld and Prof. Franco Flandoli in Pisa. From 2018 to 2021 I was a PhD student in the IRTG 2235 at Bielefeld University.

My research centers around nonlinear Fokker-Planck-Kolmogorov equations, nonlinear Markov processes and fluid dynamical equations.

With Ehsan Abedi (TU Berlin) and Florian Bechtold (Bielefeld), we recently uploaded the paper Non-uniqueness of nonlinear Markov processes in the sense of McKean associated with parabolic PDEs to arXiv. We derive a general scheme to construct infinitely many probabilistic counterparts for solutions to nonlinear PDEs by recasting the latter as different nonlinear Fokker–Planck equations and by constructing, for each of these equations, a solution to the associated McKean–Vlasov SDE with one-dimensional time marginal densities given by the PDE solution. We utilize this scheme to prove that nonlinear Markov processes are not uniquely determined by their one-dimensional time marginals, in contrast to the case of classical Markov processes, which are uniquely determined by their one-marginals. We demonstrate our results by constructing a continuum of nonlinear Markov processes with one-dimensional time marginal densities given by the Barenblatt solutions to the porous medium and $p$-Laplace equations, as well as by the fundamental solution to the heat equation. This includes a novel martingale representation for the $p$-Laplace Barenblatt solutions. We also prove that a nonlinear Markov process is uniquely determined by its two-dimensional time marginals. Moreover, for the porous medium equation, we show that the different McKean–Vlasov SDEs we investigate are consistent with corresponding gradient flow interpretations of the equation in the sense of Otto calculus.

Get in touch

I am co-organizing the 3rd Young Summer School on Stochastic Analysis in Växjö (10.-13.06.2026). If you are interested, feel free to send me an email!

I am co-organizing a conference on nonlinear PDEs, Markov processes and Dirichlet forms at the Bernoulli Center Lausanne in October. More information can be found on the conference website. If you are interested, feel free to reach out!

I will attend and talk at the 15th AIMS Conference in Athens (06.-10.07.26).