About me
I am currently Assistant Professor of Mathematics at ETH Zurich.
My research is on Elliptic 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 page for direct links to pdf).

F. Franceschini, J. Serra,
Free boundary partial regularity in the thin obstacle problem,
preprint arXiv:2112.11104. 
A. Figalli, X. RosOton, J. Serra,
The singular set in the Stefan problem,
preprint arXiv:2103.13379.
See also M. Rovrig's story in Quanta Magazine: Mathematicians Prove Melting Ice Stays Smooth, 
A. Figalli, X. RosOton, J. Serra,
Generic regularity of free boundaries for the obstacle problem,
Publ. Math. IHÉS 159 (2020), 181292. 
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 integrodifferential equations,
Duke Math. J. 165 (2016), 20792154.