Department for Applied Mathematics
University of Freiburg
79104 Freiburg im Breisgau

Office hours: on appointment

Research Interests

I am interested in problems at the interface of partial differential equations, the calculus of variations, and geometric analysis. The focus of my research is analytic, although I have implemented numerical simulations to demonstrate that new theoretical techniques can be efficiently applied in practice. My work so far has been motivated by problems arising from the study of lipid bilayers and crystal dislocations. Specifically, I have worked on phase-field approximations of Willmore's energy and on the dynamics of crystal dislocations in a model involving a fractional differential operator and a periodic potential.

Publications

• Phase Field Models for Thin Elastic Structures with Topological Constraint (with P.W. Dondl and A. Lemenant) Arch Rational Mech Anal (2016). doi:10.1007/s00205-016-1043-6 preprint
• Uniform Regularity and Convergence of Phase Fields for Willmore's Energy (with P.W. Dondl) preprint
• Helfrich's Energy and Constrained Minimisation preprint
• On the Alexandrov Topology of Sub-Lorentzian Manifolds (with I.\ Markina) Geometric Control Theory and Sub-Riemannian Geometry, Springer INdAM Series Vol. 5, Springer, Berlin Heidelberg New York, 2014 preprint

Teaching

• Functional Analysis, Summer Term 2016
• Viscosity Solutions, Summer Term 2017