Professor of Mathematics
My research sits at the intersection between Partial Differential Equations, Geometric Measure Theory, and the Calculus of Variations. In particular, I am interested in oscillation and concentration phenomena and what can be rigorously proved about their "shape". On the applied side, I am interested in the Mathematics of Material Science, in particular the theories of elasticity, elasto-plasticity and dislocations.
My research has been funded by the European Research Council (ERC), EPSRC, and the Lloyds Register Foundation.
Our group maintains the website www.ercsingularity.org, which contains details on our research, publications, and recent preprints.
Selected recent publications
- Energetic solutions to rate-independent large-strain elasto-plastic evolutions driven by discrete dislocation flow, to appear in J. Eur. Math. Soc. (JEMS), arXiv:2109.14416Link opens in a new window.
- Shape optimization of light structures and the vanishing mass conjecture (with J.-F. Babadjian, F. Iurlano), to appear in Duke Math. J., arXiv:2102.09911Link opens in a new window.
- Concentration versus oscillation effects in brittle damage (with J.-F. Babadjian, F. Iurlano), Comm. Pure Appl. Math. 74 (2021), 1803--1854, arXiv:1906.02019Link opens in a new window.
- Dimensional estimates and rectifiability for measures satisfying linear PDE constraints (with A. Arroyo-Rabasa, G. De Philippis, J. Hirsch), Geom. Funct. Anal. 29 (2019), pp 639-658, Online versionLink opens in a new window.
- Liftings, Young measures, and lower semicontinuity (with G. Shaw), Arch. Ration. Mech. Anal. 232 (2019), 1227-1328, Online versionLink opens in a new window.
- On the structure of A-free measures and applications (with G. De Philippis), Ann. of Math. 184 (2016), 1017-1039, Online versionLink opens in a new window.
I usually teach Analysis courses at the University of Warwick (e.g. PDEs, Calculus of Variations, Complex Analysis).
The book Calculus of Variations is based on my lectures at the University of Warwick on that topic and appeared with Springer in 2018: