12.06.2024 16:15 Carina Geldhauser (TU München):
Mathematical analysis of high-dimensional physical systemsMI 03.04.011 (Boltzmannstr. 3, 85748 Garching)

This talk contains two parts. Part one gives an overview of my resarch as part of the TUM Habilitation tradition. In part two, I will present my latest result.

In the first part, I will focus on a high-level overview of my results in gSQG point vortex dynamics. I will then gently flip over to some results on traveling waves in heterogeneous environments.

My latest result, which I will present in greater detail, is an fine analysis of the structure of propagating phase boundaries in a viscous diffusion equation. We characterize the relevant traveling waves, and study the two sharp-interface regimes related to two different limits, namely vanishing viscosity or the bilinear limit. This result is joint work with Michael Herrmann and Dirk Janssen.