Research Interests:

My research interests are partial differential equations, mainly from a variational point of view. In particular, I am interested in nonlinear elasticity. I also study some questions at the boundary between analysis and differential geometry.

In slightly more detail:

• I am interested in variational problems that model thin elastic sheets that form ridges and vertices where the elastic energy focuses. Here, the main task is to prove elastic free forms bounds for the free elastic energy. These problems have a strong geometric flavour. Of particular interest are variational problems for thin elastic sheets where the boundary conditions and/or the reference metric are chosen such that short maps are permissible, but there does not exist a smooth geometric immersion of the sheet into Euclidean space. Such a situation is given by a single disclination in a thin elastic sheet, for which I have proved optimal ansatz-free lower bounds (See here, here and here.)
• These questions are linked to a famous dichotomy in differential geometry: On the one hand, there is the Nash-Kuiper Theorem, stating that in every neighborhood of a short immersion of a Riemannian manifold, there exists a continuously differentiable isometric immersion (this is an instance of the so-called h-principle). On the other hand, there is the rigidity in the classical Weyl problem (which considers twice continuously differentiable isometric immersions). In between these cases, one has the isometric immersion problems in the class of maps with Hölder continuous derivatives. Which of the two (rigidity/h-principle) holds for these intermediate cases is a partly open question. Integrability properties of the Brouwer degree play an important role in the proof of the rigidity results; in a paper of mine these are investigated in some detail.
• I am also interested in the derivation of reduced models in nonlinear elasticity by Gamma-convergence. In the past, I have mainly worked on homogenization and dimension reduction limits.
• Up to the completion of my PhD thesis, I worked on topics in quantum field theory. More precisely, I did work on the operator product expansion and QFT on curved spacetimes.