## One more year Münster Research Fellow: Prof. Dr. Stephan Luckhaus

We are pleased that Prof. Dr. Stephan Luckhaus will enrich our Cluster for another year as a Münster Research Fellow. The well-known mathematician, whose research combines various mathematical fields, will contribute to the 2021 focus program "Geometry and PDEs: from theory to applications".

The new focus program aims to connect the fields of differential geometry, metric geometry, PDEs, calculus of variations, data science and numerics, and to foster the interaction between these different mathematical disciplines. The field of geometry and the areas of applied mathematics should benefit equally.

"I am certain that the focus program 2021 will provide a strong impulse for my research," says Stephan Luckhaus. "The interplay between geometry and continuum physics has been one of my long-term interests. In the past I have focused mainly on so called free boundary problems involving the mean curvature of the free boundary. Of these I am still interested in the problems of 'homogeneous nucleation'. A new focus of my research are singularities of higher codimension of the type of mechanical dislocations. Here, there are strong links to geometric measure theory."

Given his long research experience, Stephan Luckhaus contributes much profound knowledge to the focus program through his work on partial differential equations that model physical or biomedical processes. He has developed mathematical solutions to problems of water and mass transport in soil and a theoretical model for the growth of tumor cells in healthy tissue. He is well known for his achievements in harmonic maps (interpolation lemma for boundary values), elliptic-parabolic systems, fluxes in porous media, homogenization and phase transitions. His main interests are free boundary problems and many particle systems, as well as the geometric theory of nonlinear elasticity and plasticity and applied geometric measure theory.

Over the last year he has been actively involved in the programs of the cluster as a Münster Research Fellow. "Stephan Luckhaus has an overview of many areas of mathematics far beyond analysis, from stochastics to differential geometry and deep into theoretical mathematics. His insights enrich our discussions, workshops and conferences and he is a valuable contact for all of us. His holistic view of mathematics fits perfectly with the concept of Münster’s Cluster of Excellence," says Cluster spokesperson Prof Christopher Deninger.

Stephan Luckhaus has been senior professor at the University of Leipzig since October 2019, where he held the Chair of Mathematical Optimization and the Calculus of Variations until his retirement. He was awarded the Max Planck Research Prize 2003 and is an external member of the Max Planck Institute for Mathematics in the Sciences and the Academy of Sciences and Literature Mainz. In 2007 he was elected member of the German National Academy of Sciences Leopoldina and he has been senator of the mathematics section there since 2019. By the way, his career began here in Münster: in 1975 he completed his degree in mathematics, with a minor in physics, at the University of Münster.