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 (Complete list of publications)
Find all pdfs of my papers in arXiv

M. Caselli, E. Florit, J. Serra,
Yau's conjecture for nonlocal minimal surfaces,
preprint arXiv:2306.07100. 
H. Chan, S. Dipierro, E. Valdinoci, J. Serra,
Nonlocal approximation of minimal surfaces: optimal estimates from stability,
preprint arXiv:2308.06328. 
F. Franceschini, J. Serra,
Free boundary partial regularity in the thin obstacle problem,
Comm. Pure. Appl. Math., accepted. 
A. Figalli, X. RosOton, J. Serra,
The singular set in the Stefan problem,
J. Amer. Math. Soc., accepted
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 142 (2020), 10831160. 
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.