# Eva Kopfer receives the Hausdorff Memorial Prize

Bonn, January 26, 2019. Every year the Department of Mathematics ("Fachgruppe Mathematik“) rewards the best PhD thesis with the Hausdorff Memorial Prize. This year Eva Kopfer was awarded this prize with her thesis “Heat Flows on Time-Dependent Metric Measure Spaces“, which she wrote under the supervision of Karl-Thedor Sturm. In her work, she studied gradient flows (with respect to energy and entropy) in the time-dependent case. In the time-independent case, it is well-known that the solution u(t) of the heat equation is the curve (in the $L^2$ space of probability densities) for which the function $t \to E(u(t))$ decreases most rapidly where $E$ is the energy. According to a groundbreaking work by Felix Otto, this curve (regarded as a curve in the space of probability measures, provided with the so-called Wasserstein metric) also reduces the entropy most rapidly. In the time-dependent case, not only does the functional change but also the underlying geometry. Thus, a priori it is not clear what is meant here by a gradient-flow curve and what the relationship between energy and entropy looks like. Eva Kopfer was able to answer all these questions at a high level of generality. Both gradient flows are also related in this case if one considers a reversal of time. These gradient flows are used to characterize the time evolution of the metric measure spaces as so-called super-Ricci flows. This result generalizes the characterization of synthetic lower Ricci curvature bounds in the sense of Lott-Sturm-Villani to the time-dependent setting, as well as the characterization of super-Ricci flows in the case of smooth Riemannian manifolds.

In addition, the Bonn Mathematical Society („Bonner Mathematische Gesellschaft“) awards a prize for the best graduating Bachelor students in mathematics every year endowed with 250 Euro. In the academic year 2017/2018, the following three graduating Bachelor students were awarded:

• Meike Neuwohner, “Trackless Track Assignment", advisor: Jens Vygen
• Adrian Riekert, "Statistical Mechanics of a Two-Dimensional Inviscid Fluid“, advisor: Massimiliano Gubinelli
• Niklas Schlomberg, "TSP mit dynamischer Programmierung", advisor: Jens Vygen.
Karl-Theodor Sturm (PhD Advisor and HCM Director), Eva Kopfer, Martin Rumpf (Head of the Department)
Ingo Lieb (President of the Bonn Mathematical Society), Meike Neuwohner, Adrian Riekert, Niklas Schlomberg