Xavier Ros-Oton
ICREA Research Professor and Catedràtic d'Universitat
Departament de Matemàtiques i Informàtica,
Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain
email: xros at ub.edu
Selected papers
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The singular set in the Stefan problem, pdf
Alessio Figalli, Xavier Ros-Oton, Joaquim Serra,
preprint arXiv (2021).
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Stable cones in the thin one-phase problem, pdf
Xavier Fernandez-Real, Xavier Ros-Oton,
preprint arXiv (2020).
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Generic regularity of free boundaries for the obstacle problem, pdf
Alessio Figalli, Xavier Ros-Oton, Joaquim Serra,
Publ. Math. IHÉS 132 (2020), 181-292.
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Free boundary regularity for almost every solution to the Signorini problem, pdf
Xavier Fernandez-Real, Xavier Ros-Oton,
Arch. Rat. Mech. Anal. 240 (2021), 419-466.
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Stable solutions to semilinear elliptic equations are smooth up to dimension 9, pdf
Xavier Cabré, Alessio Figalli, Xavier Ros-Oton, Joaquim Serra,
Acta Math. 224 (2020), 187-252.
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Free boundary regularity in the parabolic fractional obstacle problem, pdf
Begoña Barrios, Alessio Figalli, Xavier Ros-Oton,
Comm. Pure Appl. Math. 71 (2018), 2129-2159.
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Obstacle problems for integro-differential operators: regularity of solutions and free boundaries, pdf
Luis Caffarelli, Xavier Ros-Oton, Joaquim Serra
Invent. Math. 208 (2017), 1155-1211.
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Infinite speed of propagation and regularity of solutions to the fractional porous medium equation in general domains, pdf
Matteo Bonforte, Alessio Figalli, Xavier Ros-Oton,
Comm. Pure Appl. Math. 70 (2017), 1472-1508.
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Global regularity for the free boundary in the obstacle problem for the fractional Laplacian, pdf
Begoña Barrios, Alessio Figalli, Xavier Ros-Oton,
Amer. J. Math. 140 (2018), 415-447.
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Boundary regularity for fully nonlinear integro-differential equations, pdf
Xavier Ros-Oton, Joaquim Serra,
Duke Math. J. 165 (2016), 2079-2154.
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Sharp isoperimetric inequalities via the ABP method, pdf
Xavier Cabré, Xavier Ros-Oton, Joaquim Serra,
J. Eur. Math. Soc. 18 (2016), 2971-2998.
Book
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Regularity Theory for Elliptic PDE, pdf
Xavier Fernandez-Real, Xavier Ros-Oton,
Submitted (2020).
Some expository papers
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Understanding singularities in free boundary problems, pdf
Xavier Ros-Oton, Joaquim Serra,
Matematica, Cultura e Societa 4 (2019), 107-118.
Special volume in honor of Alessio Figalli.
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Obstacle problems and free boundaries: an overview, pdf
Xavier Ros-Oton,
SeMA J. 75 (2018), 399-419.
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Boundary regularity, Pohozaev identities, and nonexistence results, pdf
Xavier Ros-Oton,
Chapter 9 in the book Recent developments in Nonlocal Theory, De Gruyter, 2018.
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Nonlocal elliptic equations in bounded domains: a survey, pdf
Xavier Ros-Oton,
Publ. Mat. 60 (2016), 3-26.
Boards and Committees
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Editorial Board member of Calc. Var. PDE (2020 - present).
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Editorial Board member of Nonlinear Analysis (2020 - present).
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President of the committee of the Catalan Mathematical Olympiad (2020 - present).
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Scientific Committee member for the Biennial Conference of the RSME 2021.
Awards
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Premio FPdGi Investigación Científica 2019 from the Fundación Princesa de Girona
Awarded anually to a young Spanish scientist under 35 years.
The prize is given by the King of Spain, and comes with a monetary award of 20,000€. -
PI of the ERC Starting Grant 'EllipticPDE' (2019 - 2024)
Awarded amount: 1,335,250€
Youngest awardee of ERC Starting Grant 2018 (among all panels in all sciences) -
PI of SNSF Research Project (2018 - 2020)
Awarded amount: 200,000CHF -
Premio Antonio Valle 2017 from the Spanish Society of Applied Mathematics
Award to the best researcher under 34 years. At age 29, I became the youngest winner of the award ever. -
Premio Jose Luis Rubio de Francia 2017 from the Real Sociedad Matemática Española
Awarded anually to a young mathematician from Spain or residing in Spain.
It is the highest distinction given by the RSME, and one of the most important prizes in Mathematics in Spain. - Awarded amount: $103,617
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Premio Vicent Caselles 2015 from the Real Sociedad Matemática Española
Spanish award to the best PhD theses in Mathematics -
Extraordinary PhD Prize from the Universitat Politecnica de Catalunya
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Premi Évariste Galois 2012 from the Societat Catalana de Matemàtiques
Silver Medals at the International Mathematical Competition for university students 2007, 2008, and 2009
Bronze Medal at the International Mathematical Olympiad 2006
For PhD students
- If you are interested on elliptic PDE:
- Book on elliptic PDE, written jointly with X. Fernandez-Real.
- Lectures by L. Caffarelli on Nonlinear Elliptic Equations (videos)
- Lecture Notes by C. Mooney on eliptic PDE.
- Book of Q. Han and F. Lin on eliptic PDE.
- Expository paper of X. Cabre.
- If you are interested on free boundary problems:
- Lecture notes of a CIME minicourse I taught in 2019.
- Lecture notes of L. Caffarelli on the obstacle problem.
- Lecture notes of B. Velichkov on the one-phase Bernoulli problem.
- Lectures by L. Caffarelli on Free Boundary Problems (videos)
- Book of A. Petrosyan, H. Shahgholian, N. Uraltseva on obstacle-type problems.
- Book of L. Caffarelli and S. Salsa on free boundary problems.
- If you are interested on integro-differential equations:
- Handwritten notes of a PhD course on integro-differential equations that I taught at UT Austin (2016): Ch 1, Ch 2, Ch 3, Ch 4.
- Nonlocal equations Wiki
- Getting acquainted with the fractional Laplacian, by N. Abatangelo and E. Valdinoci.
- Fractional thoughts, by N. Garofalo.
- Lecture notes on nonlocal equations, by L. Silvestre.
Theses
Other
- Does one have to be a genius to do maths? (by T. Tao)
- There's more to Mathematics than rigour and proofs (by T. Tao)
- The Value of Science, by R. Feynman
- Mathematics in Barcelona: Time Past, Time Future (written by the AMS in 2005)
- BGSMath
In Catalan/Spanish
- Interview by the RSME
- Interview at the newspaper 'El Pais'
- Interview at the newspaper 'El Punt Avui'
- Interview at the newspaper 'ElDiario'
- Interview at the newspaper 'El Español'
- Report at the newspaper 'Diari Ara'
- Report at the newspaper 'La Vanguardia'
- Video of a talk given at the BBVA Foundation, aimed at the general public.
- Video at the newspaper 'ABC.es'
- 'Quant cobra un matematic?', article at SCM-Noticies
- 'Matematica, ciencia i politica', article at Pensem.cat