Ranked 1st, finishing the 5 years degree in 4 years.

Transcription

1 Xavier Ros-Oton Contact Information Universität Zürich Institut für Mathematik Winterthurerstrasse 190, Zürich user.math.uzh.ch/ros-oton Birth Barcelona, April 1988 Positions Universität Zürich 09/ present Lecturer in Pure Mathematics Institut für Mathematik University of Texas at Austin 08/ /2017 R. H. Bing Instructor Department of Mathematics Education Ph.D. in Mathematics 09/ /2014 Universitat Politècnica de Catalunya (UPC) Adviser: Xavier Cabré (ICREA researcher and Professor at UPC) Master in Mathematics 09/ /2011 Universitat Politècnica de Catalunya Degree in Mathematics 09/ /2010 Universitat Politècnica de Catalunya Ranked 1st, finishing the 5 years degree in 4 years. Research interests My research focuses on elliptic and parabolic PDE. I study: - Free boundary problems - Integro-differential equations - Variational problems, stable solutions - Fully nonlinear equations - Evolution equations - Isoperimetric inequalities - Classical ODEs Honors and Awards PI of the ERC Starting Grant EllipticPDE ( ) (Awarded amount: 1,335,250 e) Youngest awardee of ERC Starting Grant 2018 (among all panels in all sciences) PI of SNSF Research Project (04/ /2020) (Awarded amount: 200,000 CHF) Antonio Valle Prize 2017 from the Spanish Society of Applied Mathematics (Awarded anually to the best researcher under 34 years. At age 29, I became the youngest winner of the award ever.) J. L. Rubio de Francia Prize 2017, Royal Spanish Mathematical Society (RSME) (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.) 1 of 9

2 PI of the NSF Analysis Grant DMS (07/ /2017) (Awarded amount: $103,617) Vicent Caselles Prize 2015 from the RSME and the BBVA Foundation (Spanish award to the best PhD theses in Mathematics) Extraordinary PhD Prize from the Universitat Politècnica de Catalunya Évariste Galois Prize 2012 from the Catalan Mathematical Society (SCM) (Best Master s Thesis award) Silver Medals at the International Mathematical Competition for University students, 2007, 2008, and 2009 Bronze Medal at the International Mathematical Olympiad (IMO), 2006 Articles and preprints [1] Higher-order boundary regularity estimates for nonlocal parabolic equations, H. Vivas Calc. Var. Partial Differential Equations 57 (2018), 111. [2] Structure and regularity of the singular set in the obstacle problem for the fractional Laplacian, N. Garofalo, preprint (Mar. 2017). [3] The obstacle problem for the fractional Laplacian with critical drift, X. Fernandez-Real, Math. Ann. 371 (2018), [4] The boundary Harnack principle for nonlocal elliptic equations in non-divergence form, Potential Anal., in press (2018). [5] Free boundary regularity in the parabolic fractional obstacle problem, B. Barrios, A. Figalli, Comm. Pure Appl. Math., in press (2018). [6] On the regularity of the free boundary for the p-laplacian obstacle problem, A. Figalli, B. Krummel, J. Differential Equations 263 (2017), [7] The structure of the free boundary in the fully nonlinear thin obstacle problem, Adv. Math. 316 (2017), [8] Obstacle problems for integro-differential operators: regularity of solutions and free boundaries, L. Caffarelli, Invent. Math. 208 (2017), [9] Boundary regularity estimates for nonlocal elliptic equations in C 1 and C 1,α domains, Ann. Mat. Pura Appl. 196 (2017), [10] Regularity theory for general stable operators: parabolic equations, X. Fernandez-Real, J. Funct. Anal. 272 (2017), [11] Infinite speed of propagation and regularity of solutions to the fractional porous medium equation in general domains, 2 of 9

3 M. Bonforte, A. Figalli, Comm. Pure Appl. Math. 70 (2017), [12] Global regularity for the free boundary in the obstacle problem for the fractional Laplacian, B. Barrios, A. Figalli, Amer. J. Math. 140 (2018), [13] A one-dimensional symmetry result for a class of nonlocal semilinear equations in the plane, F. Hamel, Y. Sire, E. Valdinoci, Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), [14] Pohozaev identities for anisotropic integro-differential operators, E. Valdinoci, Comm. Partial Differential Equations 42 (2017), [15] The Dirichlet problem for nonlocal operators with singular kernels: convex and non-convex domains, E. Valdinoci, Adv. Math. 288 (2016), [16] Regularity theory for general stable operators, J. Differential Equations 260 (2016), [17] Boundary regularity for fully nonlinear integro-differential equations, Duke Math. J. 165 (2016), [18] Nonlocal problems with Neumann boundary conditions, S. Dipierro, E. Valdinoci, Rev. Mat. Iberoam. 33 (2017), [19] Boundary regularity for the fractional heat equation, X. Fernández-Real, Rev. Acad. Cienc. Ser. A Math. 101 (2016), [20] Local integration by parts and Pohozaev identities for higher order fractional Laplacians, Discrete Contin. Dyn. Syst. A 35 (2015), [21] Regularity for the fractional Gelfand problem up to dimension 7, J. Math. Anal. Appl. 419 (2014), [22] Nonexistence results for nonlocal equations with critical and supercritical nonlinearities, Comm. Partial Differential Equations 40 (2015), [23] The extremal solution for the fractional Laplacian, Calc. Var. Partial Differential Equations 50 (2014), [24] Sharp isoperimetric inequalities via the ABP method, X. Cabré, J. Eur. Math. Soc. 18 (2016), [25] The Pohozaev identity for the fractional Laplacian, Arch. Rat. Mech. Anal. 213 (2014), of 9

4 [26] The Dirichlet problem for the fractional Laplacian: regularity up to the boundary, J. Math. Pures Appl. 101 (2014), [27] Sobolev and isoperimetric inequalities with monomial weights, X. Cabré, J. Differential Equations 255 (2013), [28] Regularity of stable solutions up to dimension 7 in domains of double revolution, X. Cabré, Comm. Partial Differential Equations 38 (2013), [29] Existence of periodic solutions with nonconstant sign in a class of generalized Abel differential equations, J. M. Olm, Discrete Contin. Dyn. Syst. A 33 (2013), [30] On a factorization of Riemann s ζ function with respect to a quadratic field and its computation, Rev. Acad. Cienc. Ser. A Math. 106 (2012), [31] Periodic solutions with nonconstant sign in Abel equations of second kind, J. M. Olm, T. M. Seara, J. Math. Anal. Appl. 381 (2011), [32] Stable inversion of Abel equations: application to tracking control in DC-DC nonminimum phase boost converters, J. M. Olm, Y. B. Shtessel, Automatica J. IFAC 47 (2011), [33] Approximate tracking of periodic references in a class of bilinear systems via stable inversion, J. M. Olm, Discrete Contin. Dyn. Syst. Ser. B 15 (2011), Expository papers, short notes, book chapters [34] Free boundaries and obstacle problems: an overview, SeMA J. 75 (2018), to appear. [35] Boundary regularity, Pohozaev identities, and nonexistence results, Chapter 9 in Recent developments in the Nonlocal Theory, De Gruyter, [36] Nonlocal elliptic equations in bounded domains: a survey, Publ. Mat. 60 (2016), [37] Euclidean balls solve some isoperimetric problems with nonradial weights, X. Cabré, C. R. Math. Acad. Sci. Paris 350 (2012), [38] Fractional Laplacian: Pohozaev identity and nonexistence results, C. R. Math. Acad. Sci. Paris 350 (2012), of 9

5 Invited talks at conferences Barcelona Analysis Conference 2019 Plenary talk. Universitat de Barcelona, June Probability & Analysis 2019 Plenary talk. Conference Center of the Polish Academy of Sciences (Bȩdlewo, Poland), May Biennial Conference of the Royal Spanish Mathematical Society Plenary talk. Santander (Spain), February Nonlocal interactions: Dislocations and beyond University of Bath, June Maxwell Symposium in PDEs International Centre for Mathematical Sciences (Edinburgh), December Conference on Partial Differential Equations KTH Stockholm, December Mathematical approaches to complex systems: Statistical mechanics and PDEs Convento da Arrábida (Portugal), July XXV Congreso de Ecuaciones Diferenciales y Aplicaciones Plenary talk on the occasion of the Antonio Valle Prize Cartagena (Spain), June Warwick EPSRC Symposium: Non-local equations and fractional diffusion Warwick University, May Fall Meeting of the American Mathematical Society Special session on New developments in the analysis of nonlocal operators. Minneapolis, October rd Conference on Nonlocal Operators and PDEs Plenary talk. Conference Center of the Polish Academy of Sciences (Bȩdlewo, Poland), June Nonlocal Variational Problems and PDEs Pacific Institute of Mathematical Sciences (Vancouver), June Recent trends on elliptic nonlocal equations Fields Institute (Toronto), June Spring Meeting of the American Mathematical Society Special session on Fractional calculus and nonlocal operators. East Lansing (Michigan), March th AIMS Conference on Dynamical Systems, Differential Equations and Applications Special session on Geometric variational problems. Madrid, July th AIMS Conference on Dynamical Systems, Differential Equations and Applications Special session on Nonlocal problems and related topics. Madrid, July Recent Advances in Nonlocal and Nonlinear Analysis, Theory and Applications ETH Zürich, June Meeting on PDEs and Applications Girona, June of 9

6 Workshop on Non-Standard Diffusions Austin, May Workshop on Partial Differential Equations and applications Pisa, February Workshop on Nonlinear equations Universidad Carlos III Madrid, October Congress of young researchers of the Real Sociedad Matemática Española Special session on PDEs. Sevilla, September Conference of young researchers of the Societat Catalana de Matemàtiques Special session on Analysis and PDEs. Barcelona, October Barcelona-Boston-Tokyo Number Theory Congress in Memory of Fumiyuki Momose Barcelona, May Invited talks at seminars, colloquiums Universitat de Barcelona. Colloquium IMUB. November Wuhan Institute of Physics & Mathematics, Chinese Academy of Sciences. July Wuhan University. July University of Texas at Austin. Analysis seminar. May University of Houston. PDE seminar. April Universitat Politècnica de Catalunya. Colloquium FME-UPC. April Universidad Autónoma de Madrid. PDE seminar. March Instituto de Ciencias Matemáticas. PDE s & Fluid Mechanics seminar. March ETH / Universität Zürich. Zürich Graduate Colloquim. February Institut des Hautes Études Scientifiques. Séminaire Laurent Schwartz. January Universität Basel. Analysis seminar. December Universidad Autónoma de Madrid. Colloquium. October Massachusetts Institute of Technology. PDE/Analysis seminar. April ETH Zürich. Analysis seminar. March École Polytechnique Fédérale de Lausanne. Colloquium. March Courant Institute, New York University. Analysis seminar. February Universitat Politècnica de Catalunya. PDE Seminar. December Hausdorff Center for Mathematics (Bonn). December University of California Los Angeles. Analysis seminar. December Universität Zürich. November Rice University. Colloquium. November University of Texas at Austin. Analysis seminar. October Columbia University. Analysis seminar. February Michigan State University. Analysis seminar. October University of Copenhagen. Analysis and Geometry seminar. June African Institute of Mathematical Sciences (Senegal). PDE seminar. June University of Chicago. PDE seminar. February Universidad del País Vasco (UPV/EHU). Analysis seminar. May Universität Basel. Analysis seminar. December of 9

7 Università di Roma Tor Vergata. PDE seminar. November Universitat Politècnica de Catalunya. PDE seminar. April Basque Center for Applied Mathematics. PDE seminar. February Minicourses Huazhong University of Science and Technology (China). 16h Minicourse on Nonlocal PDE. July Research projects ERC Starting Grant / /2024 Project: Regularity and singularities in elliptic PDE s PI: X. Ros-Oton Awarded amount: 1,335,250 e SNSF Research Project (Switzerland) 04/ /2020 Project: Integro-differential elliptic equations PI: X. Ros-Oton Awarded amount: 200,000 CHF Start-up Grant J. L. Rubio de Francia 10/ /2020 BBVA Foundation PI: X. Ros-Oton Amount: 35,000e NSF Analysis Grant DMS (USA) 07/ /2017 Project: Regularity theory for elliptic equations and free boundaries PI: X. Ros-Oton Awarded amount: $103,617 Start-up research and travel money 09/ /2017 Department of Mathematics, UT Austin Amount: $15,000 Organization of conferences PDE s and Geometric Measure Theory Organizers: A. Figalli, J. Serra. Zürich, October Teaching Universität Zürich Fall 2018 Integro-differential elliptic equations, MAT695 (PhD course, 56 hours) Universität Zürich Fall 2017 Topics on Elliptic PDE s, MAT831 (PhD course, 56 hours) University of Texas at Austin Spring 2017 Graduate Reading Course, M 396D (Graduate student: Hernán Vivas) University of Texas at Austin Spring of 9

8 Differential Equations, M 427J University of Texas at Austin Fall 2016 Nonlocal Elliptic Equations, M 393C (PhD course, 42 hours) University of Texas at Austin Spring 2016 Multivariable Calculus, M 408M University of Texas at Austin Fall 2015 and Spring 2016 Graduate Reading Course, M 396D (Graduate student: Xavier Fernández-Real) University of Texas at Austin Fall 2015 Differential Calculus for Science, M 408N University of Texas at Austin Spring 2015 Differential and Integral Calculus, M 408C University of Texas at Austin Fall 2014 Differential Calculus, M 408K UPC, Master in Mathematics Spring 2014 Advanced Partial Differential Equations UPC, Degree in Mathematics Spring 2013 Functional Analysis Scientific and administrative responsibilities Reviewer of research proposals for different national science agencies: DFG (Germany); NCN (Poland); FONDECYT (Chile). Referee for several journals, including: Acta Math.; Invent. Math.; Duke Math. J.; Comm. Pure Appl. Math.; J. Eur. Math. Soc.(2); Arch. Rat. Mech. Anal.; Geom. Funct. Anal.; J. Math. Pures Appl.; Anal. PDE (3); Int. Math. Res. Not.; J. Funct. Anal. (4); Trans. AMS (2); Ann. Inst. H. Poincaré; Comm. Math. Phys.; J. Differential Equations; Proc. Lond. Math. Soc.; Calc. Var. PDE (3); Ann. Mat. Pura Appl.; Comm. PDE (4); Publ. Mat.; Rev. Mat. Iberoam.; J. Math. Anal. Appl. (2); J. Lond. Math. Soc.; SIAM J. Math. Anal.; Proc. Amer. Math. Soc.; Nonlinear Anal.; Studia Math.; Com. Contemp. Math.(3); Arch. Math.; Nonl. Diff. Eq. Appl.; Rev. Acad. Cienc. Math.; Manuscr. Math.; Math. Nachr. (2); Referee for Springer books (2) Science outreach & Media Lecture at the BBVA Foundation aimed at public outreach. Title: Las ecuaciones que mueven el mundo Madrid, April Interview for the newspaper El Español (April 2018) Video-Interview for SwissInfo (August 2018) 8 of 9

9 Participation as a scientific expert for DivulCat (since 2018) This is a project for science outreach, organized by Enciclopèdia.cat Citations More than 1200 citations in Google Scholar; more than 400 in MathSciNet. The paper The Dirichlet problem for the fractional Laplacian: regularity up to the boundary is one of the top 3 most cited papers of the year 2014 in MathSciNet (among all papers in mathematics). 9 of 9