Leon Bungert is a postdoctoral researcher at Hausdorff Center for Mathematics at the Rhenish Friedrich Wilhelm University of Bonn. Leon received his PhD summa cum laude from the University of Erlangen in September 2020 under supervision of Martin Burger and his thesis was awarded with the Biennial French-German Mathematics in Imaging PhD Prize. He does research in applied analysis, connecting techniques from inverse problems and PDEs on graphs with applications in data science and imaging.
Leon has investigated variational regularization methods for ill-posed inverse problems, proving novel convergence rates and studying their parameter dependence in large generality. Furthermore, he has related fine properties of gradient flows to nonlinear eigenvalue problems, thereby deriving new algorithms for tackling graph clustering problems and the computation of geodesic distance functions. He has also investigated continuum limits of graphs-based semi-supervised learning and derived novel regularization methods for neural networks.