Kilian Koch

Kilian Koch is a mathematics researcher and doctoral researcher at the Chair of Applied Analysis at RWTH Aachen University, where he works within Collaborative Research Centre 1481, “Sparsity and Singular Structures.” His research focuses on gradient flows in geometric analysis, especially the well-posedness and singular behaviour of half-harmonic map heat flows. Supported by the German Research Foundation through CRC 1481’s project on singularity formation in dissipative harmonic flows, Koch contributes to research at the intersection of geometric analysis and singular partial differential equations.

His scholarly work includes preprints on well-posedness for half-harmonic map heat flows with rough initial data and thresholding schemes for these flows. The latter investigates a numerical approach using the Poisson kernel and pointwise normalization, with results on convergence and energy dissipation. Koch also presents his research at seminars and workshops, and has helped organize a workshop on geometric analysis, singular PDEs and numerics. His website provides access to publications, talk information and slides, a research profile, CV, and software links.