Heat Flow, Mean Curvature Flow and Their Related Schemes - Successful dissertation by Anton Ullrich

We congratulate Anton Ullrich on the successful defense of his dissertation: “Heat Flow, Mean Curvature Flow and Their Related Schemes”. His next career step will take him to Carnegie Mellon University in Pittsburgh, PA, United States, as a postdoctoral researcher.

In his research, Anton studied two parabolic partial differential equations (PDEs) and their related schemes. He focused on the heat flow and the mean curvature flow. Both can be used in a wide range of applications in the natural sciences and mathematics:

“The heat equation, also called the heat flow, is one of the most fundamental parabolic PDEs and comes from the description of the dissipation of heat in a (homogeneous) medium. Mean curvature flow on the other hand describes the evolution of surfaces by a relaxation through surface tension. Formally, this flow can be seen as a gradient flow of the area functional. This observation gives rise to the applications which span, for instance: grain growth, the description of annealing, descriptions of the boundary of black holes as minimal surfaces, image processing algorithms, fluid simulations, population genetics and classifier / clustering algorithms.”

After successfully completing his bachelor's and master's degrees at the University of Bonn, Anton was a PhD student in Felix Otto's group from 2022 to 2025. After successfully completing his dissertation, he is now working as a postdoctoral researcher at Carnegie Mellon University, Pittsburgh, PA, United States: “In the future, I would like to remain in academia, but you can never guarantee that,” says Anton. 

We're wishing you good luck and all the best for the future!