About me
I am currently SNF Ambizione Fellow at ETH.
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 integrodifferential equations (integration by part type identities with singular boundary terms, regularity for fully nonlinear equations)
 Reactiondiffusion 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. RosOton, J. Serra,
Generic regularity of free boundaries for the obstacle problem,
Publ. Math. IHÉS, to appear. 
X. Cabré, A. Figalli, X. RosOton, J. Serra,
Stable solutions to semilinear elliptic equations are smooth up to dimension 9,
Acta Math., 224 (2020), 187252. 
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 BVestimates for nonlocal minimal surfaces,
J. Differential Geom. 112 (2019), 447504. 
L. Caffarelli, X. RosOton, J. Serra,
Obstacle problems for integrodifferential operators: regularity of solutions and free boundaries,
Invent. Math. 208 (2017), 11551211.  X. RosOton, J. Serra,
Boundary regularity for fully nonlinear integro differential equations,
Duke Math. J. 165 (2016), 20792154.