About me

I am currently SNF Ambizione Fellow at ETH Zurich (Switzerland).

CV

My research is on elliptic and parabolic Partial Differential Equations.
The main research topics in which I have worked are:

• Regularity of phase transitions (and its conection with minimal surface theory)
• Free boundary regularity and study of singularities in the classical obstacle problem
• Analysis of elliptic nonlinear integro-differential equations

Selected papers from the last 5 years (all of my papers are available at arXiv)

• A. Figalli, X. Ros-Oton, J. Serra,
  Generic regularity of free boundaries for the obstacle problem,
  preprint arXiv:1912.00714.

• X. Cabré, A. Figalli, X. Ros-Oton, J. Serra,
  Stable solutions to semilinear elliptic equations are smooth up to dimension 9,
  Acta Math., to appear.

• 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., published online.

• 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.