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.