Teaching Responsibilities 2018/19:
Term 2: MA4G6 Calculus of Variations.
See www.ercsingularity.org for details.
Textbook "Calculus of Variations" (Springer 2018)
See www.calculusofvariations.com for details.
Most of my research sits at the intersection between Partial Differential Equations, Geometric Measure Theory, Harmonic Analysis, and the Calculus of Variations. In particular, I am interested in oscillation and concentration phenomena and what can be rigorously proved about their "shape".
Recent publications and preprints
Please see here.
- Dimensional estimates and rectifiability for measures satisfying linear PDE constraints (with A. Arroyo-Rabasa, G. De Philippis, J. Hirsch), to appear in Geom. Funct. Anal., arXiv:1811.01847.
- Liftings, Young measures, and lower semicontinuity (with G. Shaw), to appear in Arch. Ration. Mech. Anal., 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.
- Lower semicontinuity for integral functionals in the space of functions of bounded deformation via rigidity and Young measures, Arch. Ration. Mech. Anal. 202 (2011), 63-113. Online version.
- Characterization of generalized gradient Young measures in W1,1 and BV (with J. Kristensen), Arch. Ration. Mech. Anal. 197 (2010), 539-598. Online version.
A complete list of publications can be found in my CV.