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, including the theories of Elasticity and Elasto-plasticity.
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
- Concentration versus oscillation effects in brittle damage (with J.-F. Babadjian, F. Iurlano), to appear in Comm. Pure Appl. Math., arXiv:1906.02019.
- 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 version.
- Liftings, Young measures, and lower semicontinuity (with G. Shaw), Arch. Ration. Mech. Anal. 232 (2019), 1227-1328, Online version.
- On the structure of A-free measures and applications (with G. De Philippis), Ann. of Math. 184 (2016), 1017-1039, Online version.
- Directional oscillations, concentrations, and compensated compactness via microlocal compactness forms, Arch. Ration. Mech. Anal. 215 (2015), 1-63. Online version.
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:
See www.calculusofvariations.com for details.