I did my Ph.D. under the supervision of S. Müller at the University of Bonn. Currently I am a Research Fellow in the University of Warwick as part of the research group SINGULARITY led by Filip Rindler.
Teaching Responsibilities 2019/20:
Term 2: MA3G1 Theory of PDEs
Areas of specialization
- Calculus of Variations
- Geometric Measure Theory
- Regularity theory of Minimal Surfaces and their generalizations
- Classical and stochastic homogenization theory
During my short career I have developed a great interest for these topics:
- Lower semicontinuity of integral functionals and quasiconvexity
- Rigidity and fine properties of PDE constrained structures
- Regularity theory of elliptic PDE's
- Convex Analysis and Harmonic Analysis methods for variational problems
I am also very interested in learning optimal transport, convex integration techniques, and Riemannian geometry.
- Debye screening for the stationary Vlasov-Poisson equation in interaction with a point charge (with R. Winter)
- On the fine properties of elliptic operators (with A. Skorobogatova)
- Characterization of generalized Young measures generated by A-free measures
- Generalized multi-scale Young measures (joint work with J. Diermeier)
to appear in SIAM J. Math. Anal.
- An elementary approach to the dimension of measures satisfying a first-order linear PDE constraint
Proc. Amer. Math. Soc. 148(1) (2020)
- Dimensional estimates and rectifiability for measures satisfying linear PDE constraints (joint work with G. De Philippis, J. Hirsch, and F. Rindler)
Geom. Funct. Anal. 29(3) (2019)
- Lower semicontinuity and relaxation of linear-growth integral functionals under PDE constraints (joint work with G. De Philippis and F. Rindler)
to appear in Adv. Calc. Var.
- Relaxation and optimization for linear-growth convex integral functionals under PDE constraints
J. of Funct. Anal. 273 (2017)
- Regularity for free interface variational problems in a general class of gradients
Calc. Var. PDE's 55 (2016)