About me

I am currently SNF Ambizione Fellow at ETH.

CV

My research is on elliptic and parabolic Partial Differential Equations.
More precisely:

• Stable interfaces (phase transitions and minimal surfaces)
• Free boundaries (the singular sets in the obstacle problem and the Stefan problem)
• Elliptic and parabolic integro-differential equations (integration by part type identities with singular boundary terms, regularity for fully nonlinear equations)
• Reaction-diffusion equations, isoperimetric problems

Selected papers from the last 5 years (all of my papers are available at arXiv; see also the Publications and Preprints page for direct links to pdf).

• A. Figalli, X. Ros-Oton, J. Serra,
  Generic regularity of free boundaries for the obstacle problem,
  Publ. Math. IHÉS, to appear.

• X. Cabré, A. Figalli, X. Ros-Oton, J. Serra,
  Stable solutions to semilinear elliptic equations are smooth up to dimension 9,
  Acta Math., 224 (2020), 187-252.

• A. Figalli, J. Serra,
  On the fine structure of the free boundary for the classical obstacle problem,
  Invent. Math. 215 (2019), 311–366.

• A. Figalli, J. Serra,
  On stable solutions for boundary reactions: a De Giorgi type result in dimension 4+1,
  Invent. Math. 219 (2020), 153–177.

• S. di Pierro, J. Serra, E. Valdinoci,
  Improvement of flatness for nonlocal phase transitions,
  Amer. J. Math, to appear.

• E. Cinti, J. Serra, E. Valdinoci,
  Quantitative flatness results and BV-estimates for nonlocal minimal surfaces,
  J. Differential Geom. 112 (2019), 447-504.

• L. Caffarelli, X. Ros-Oton, J. Serra,
  Obstacle problems for integro-differential operators: regularity of solutions and free boundaries,
  Invent. Math. 208 (2017), 1155-1211.

• X. Ros-Oton, J. Serra,
  Boundary regularity for fully nonlinear integro- differential equations,
  Duke Math. J. 165 (2016), 2079-2154.