About me

I am currently Assistant Professor of Mathematics at ETH Zurich.

CV

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 integro-differential equations (integration by part type identities with singular boundary terms, regularity for fully nonlinear equations)
• Reaction-diffusion 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. Ros-Oton, 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. Ros-Oton, J. Serra,
  Generic regularity of free boundaries for the obstacle problem,
  Publ. Math. IHÉS 159 (2020), 181-292.

• 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 142 (2020), 1083-1160.

• 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.