CURRICULUM VITAE OF PABLO RAUL´ STINGA

A. Personal data • Surname: STINGA. • Names: Pablo Ra´ul. • Address: Department of Mathematics, The University of Texas at Austin, 1 University Station C1200 Austin , TX 78712-1202, United States of America. • e-mail: [email protected] • Actual position: Bing Instructor at Department of Mathematics, The University of Texas at Austin, United States of America.

B. Degrees held • Mar. 2000 – Dec. 2005 Degree in Mathematical Sciences, National University of San Luis (UNSL), Argentina. • Oct. 2006 – Nov. 2007 Master in Mathematics and Applications, Autonomous University of Madrid, . • Oct. 2006 – Jun. 2010 PhD in Mathematics with European Mention (Summa Cum Laude), Autonomous University of Madrid, Spain. PhD Thesis title: “Fractional Powers of Second Order Partial Differential Operators: Extension Problem and Regularity Theory”. Supervisor: Prof. Dr. Jos´eLuis Torrea.

C. Prizes and honors • 2005 Prize from UNSL for best GPA at degree in Mathematics: 9.90/10.00. • Dec. 2005 Prize from UNSL for best GPA among all degrees at National University of San Luis, Argentina.

D. Competitive grants/contracts awarded • Grant for undergraduate studies from UNSL for best GPA in high school (Mar. 2001 to Dec. 2001). • Grant for undergraduate studies from YPF Foundation (Argentina) for best GPA in the first year of undergraduate studies (Mar. 2002 to Mar. 2006). • Grant to participate at IMPA Mathematical Summer School at Istituto de Matematica Pura e Aplicada (IMPA), Rio de Janeiro, Brazil (Jan.–Feb. 2005). • Grant to participate at Third Mathematical Engineering Summer School at University of Con- cepci´on,Chile (Jan. 2006). • Postgraduate grant for PhD studies from National Council of Scientific and Technological Research CONICET, Argentina (Dec. 2005 – rejected by YPF Foundation PhD studies grant). • Postgraduate “Jos´eA. Estenssoro” grant for PhD studies from YPF Foundation, Argentina (Mar. 2006 – rejected after 6 months by Spanish Government’s grant for PhD studies in Spain). • Postgraduate grant for PhD studies form Spanish Government “Formation of Researcher Staff” (FPI) (Oct. 2006 – Sep. 2010). • Research grant from Mathematics Department of University of , Spain, for postdoctoral research (Oct. to Dec. 2010). • Research contract from Mathematics and Computation Department of University of , Spain, for postdoctoral research (Apr. to Oct. 2011). • Research contract from Mathematics and Computation Department of , Spain, for postdoctoral research (Feb. to Aug. 2012).

E. Teaching experience in Mathematics – Tutoring • 2001 High school professor in Mathematics at San Luis, Argentina. • Mar. 2004 – Dec. 2005 Tutor for new undergraduate students at National University of San Luis, Argentina. • 2002 – 2006 Teaching assistant in Mathematics at National University of San Luis, Argentina, teaching Discrete Mathematics (1st year of Mathematics Degree) and Probability and Statistics (2nd year of Mathematics Degree). • Feb. 2011 – Sep. 2011 Honorary professor in Mathematics at Autonomous University of Madrid, Spain, teaching Calculus in Several Variables (1st year of Physics Degree).

Date: April 2012. 1 2 CURRICULUM VITAE OF PABLO RAUL´ STINGA

• Fall 2012 Integral Calculus for Science M408S at The University of Texas at Austin (USA).

F. Present research areas - Keywords Fractional Laplacians and Fractional Schr¨odingerOperators, Regularity Theory (Schauder and H¨olderEsti- mates, Harnack Inequalities), Harmonic Analysis of Orthogonal Expansions and Schr¨odingerOperators, Elliptic and Parabolic Partial Differential Equations, Semigroup Theory, Approximations for Stochastic Partial Differ- ential Equations.

G. Publications and preprints 1. P. R. Stinga and J. L. Torrea, Extension problem and Harnack’s inequality for some fractional operators, Comm. Partial Differential Equations 35 (2010), 2092–2122. 2. P. R. Stinga and J. L. Torrea, Regularity theory for the fractional harmonic oscillator, J. Funct. Anal. 260 (2011), 3097–3131. 3. I. Abu-Falahah, P. R. Stinga and J. L. Torrea, Square functions associated to Schr¨odingeroperators, Studia Math. 203 (2011), 171–194. 4. T. Ma, P. R. Stinga, J. L. Torrea and C. Zhang, Regularity properties of Schr¨odingeroperators, J. Math. Anal. Appl. 388 (2012), 817–837. 5. O.´ Ciaurri, L. Roncal and P. R. Stinga, Fractional integrals on compact Riemannian symmetric spaces of rank one, Adv. Math. 235 (2013), 627–647. 6. P. R. Stinga and C. Zhang, Harnack’s inequalities for fractional nonlocal equations, Discrete Contin. Dyn. Syst. 33 (2013), 3153–3170. 7. J. J. Betancor, R. Crescimbeni, J. C. Fari˜na,P. R. Stinga and J. L. Torrea, A T 1 criterion for Hermite- n Calder´on-Zygmund operators on the BMOH (R ) space and applications, Ann. Sc. Norm. Super. Pisa Cl. Sci. (2011), accepted for publication. 8. T. Ma, P. R. Stinga, J. L. Torrea and C. Zhang, Regularity estimates in H¨olderspaces for Schr¨odinger operators via a T 1 theorem, Ann. Mat. Pura Appl. (2012), accepted for publication. 9. I. Gy¨ongyand P. R. Stinga, The rate of convergence of Wong–Zakai approximations for stochastic partial differential equations, Proceedings of the Seventh Seminar on Stochastic Analysis, Random Fields and Applications, Ascona 2011, accepted for publication.

10. L. Roncal and P. R. Stinga, Fractional Laplacian on the torus, (2012) submitted. 11. I. Abu-Falahah, P. R. Stinga and J. L. Torrea, A note on the almost everywhere convergence to initial data for some evolution equations, (2012) submitted. 12. J. E. Gal´e,P. J. Miana and P. R. Stinga, Extension problem for fractional operators: semigroups and wave equations, (2012), submitted.

13. P. L. De N´apoli and P. R. Stinga, The fractional Laplacian on the sphere, in preparation. 14. J. Dziuba´nski,M. Preisner, L. Roncal and P. R. Stinga, Hardy spaces for Fourier-Bessel expansions, in preparation. 15. J. J. Betancor, A. Castro and P. R. Stinga, The fractional Bessel equation in H¨olderspaces, in prepara- tion. 16. J. J. Betancor, R. Crescimbeni, P. R. Stinga and J. L. Torrea, The geometry of Banach spaces through Carleson measures in the Schr¨odingercontext, in preparation. 17. J. J. Betancor, A. Castro, J. C. Fari˜na,L. Rodr´ıguez-Mesaand P. R. Stinga, Triebel-Lizorkin spaces for some orthogonal expansions, in preparation. 18. F. J. Mart´ın-Reyes, P. R. Stinga and J. L. Torrea, One sided square functions and BMO, in preparation. 19. F. J. Mart´ın-Reyes, P. R. Stinga and J. L. Torrea, Fractional one sided Laplacians, in preparation.

H. Presentations in congresses • Scientific communication at Annual Meeting of the Argentinean Mathematical Union UMA 2009 – LIX Scientific Communications Meeting, Mar del Plata (Argentina), Sep. 21–26, 2009. • Invited conference at XII Real and Complex Analysis Meetings 2010 – XII EARCO, Haro (Spain), Apr. 22–24, 2010. • Contributed talk at Harmonic Analysis and Orthogonal Systems IV, Bedlewo (Poland), Sep. 19–24, 2010. • Invited conference at 22nd International Workshop on Operator Theory and its Applications IWOTA 2011, Sevilla (Spain), Jul. 3–9, 2011. • Invited conference at Workshop of Young Researchers in Mathematics 2011, Universidad Complutense de Madrid (Spain), Sep. 21–23, 2011. • Invited conference at VI Research Meeting in Approximation Theory, EITA 2011, Canfranc (Spain), Oct. 21–23, 2011. CURRICULUM VITAE OF PABLO RAUL´ STINGA 3

• Contributed talk at 9th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial 2012, El Escorial (Spain), June 11–15, 2012. • Poster at Nonlocal Operators: Analysis, Probability, Geometry and Applications, ZiF Bielefeld (Germany), Jul. 9–14, 2012. • Scientific communication at IV Latinamerican Congress of Mathematicians, CLAM 2012, C´ordoba(Ar- gentina), Aug. 6–10, 2012. • Contributed talk at Special Functions, Partial Differential Equations and Harmonic Analysis, a conference in honor of Calixto P. Calder´on, Roosevelt University, Chicago (USA), Nov 16–18, 2012.

I. Invited seminars • “Sobolev spaces associated to the harmonic oscillator” at Institute of Applied Mathematics San Luis (IMASL) of National University of San Luis (Argentina), Mar. 2009. • “The fractional harmonic oscillator: characterization via an extension problem, Harnack’s inequality and regularity theory” at Mathematical Analysis Department of (Spain), Dec. 2009. • “The extension problem for fractional powers of general second order partial differential operators” at Institute of Applied Mathematics of Litoral (IMAL) of National University of Litoral (Argentina), Feb. 2010. • “Extension problem and Harnack’s inequality for some fractional operators” at Mathematics Department of Autonomous University of Madrid (Spain), Feb. 2010. • “El rol del semigrupo del calor en problemas que involucran operadores fraccionarios” at Jos´eLuis Rubio de Francia Seminar of (Spain), May 2010. • “Fractional powers of second order partial differential operators: extension problem and regularity theory” at Mathematics Department of Autonomous University of Madrid (Spain), May 2010. • “Fractional powers of second order partial differential operators: extension problem and regularity theory” at TU Delft Applied Mathematics Colloquium (The ), Sep. 2010. • “Fractional Laplacians: extension problem and regularity theory” at Mathematics Department of University of Buenos Aires (Argentina), Nov. 2010. • “Funciones cuadrado asociadas a operadores de Schr¨odinger” at Jos´eLuis Rubio de Francia Seminar of University of Zaragoza (Spain), Dec. 2010. • “Regularity for fractional operators” at Mathematics and Computation Department of University of La Rioja (Spain), May 2011. • “Fractional powers of second order partial differential operators: extension problem and regularity theory” at Institute of Applied Mathematics San Luis (IMASL) of National University of San Luis (Argentina), May 2011. • “Square functions for Schr¨odingeroperators” at Mathematical Analysis Department of University of La Laguna (Spain), Jun. 2011. • “Regularity of fractional Schr¨odingeroperators through Harmonic Analysis techniques” at Mathematical Analysis Department of University of La Laguna (Spain), Nov. 2011. • “Regularity estimates through semigroups and harmonic analysis: The case of the Schr¨odingeroperator” at Mathematics and Computation Department of University of La Rioja (Spain), Jan. 2012. • “Regularidad para ecuaciones diferenciales locales y fraccionarias” at Jos´eLuis Rubio de Francia Seminar of University of Zaragoza (Spain), Feb. 2012. • “Semigroups and Hardy and H¨older spaces” at Mathematical Analysis Department of University of M´alaga (Spain), Jun. 2012. • “Fractional Laplacian on the torus” at Department of Mathematics and Applications “Renato Caccioppoli” of Universit`adegli Studi di Napoli “Federico II” of Naples (Italy), Jul. 2012.

J. Participation in research projects • Dec. 2005 – Dec. 2008 “M´etodos espectrales y vectoriales en an´alisis arm´onico”(Vector and spectral methods in harmonic analysis) funded by Spanish Ministry of Education and Science. PI: J. L. Torrea. • Jan. 2009 – Dec. 2011 “Teor´ıaespectral de semigrupos y su repercusi´onen an´alisisarm´onico”(Spectral theory of semigroups and its impact in harmonic analysis) funded by Spanish Ministry of Science and Innovation. PI: J. L. Torrea. • Oct. 2010 – Dec. 2010 “An´alisismatem´aticoy aplicaciones” (Mathematical analysis and applications) funded by Arag´on’sGovernment Direction, Spain. PI: J. Bastero. • Oct. 2012 – Dec. 2014 “Teor´ıaespectral. Semigrupos y aplicaciones a EDPs” (Spectral theory. Semigroups and applications to PDEs) funded by Spanish Ministry of Economy and Competitiveness. PI: J. L. Torrea.

K. Research stays 4 CURRICULUM VITAE OF PABLO RAUL´ STINGA

• Feb. 2008 – Mar. 2008 Two months at the School of Mathematics, University of Edinburgh (United Kingdom). • Sep. 2009 One week at Applied Mathematics Institute of Litoral (IMAL), National University of Litoral (Argentina). • Dec. 2009 One week at Mathematical Analysis Department, University of La Laguna (Spain). • Feb. 2010 Two weeks at Applied Mathematics Institute of Litoral (IMAL), National University of Litoral (Argentina). • Mar. 2010 One month at the School of Mathematics, University of Edinburgh (United Kingdom). • Apr. 2010 One month at Isaac Newton Institute of Mathematical Sciences, University of Cambridge (United Kingdom). • May 2010 One week at Mathematical Analysis Department, University of Zaragoza (Spain). • Jul. 2010 One week at the School of Mathematics, University of Edinburgh (United Kingdom). • Sep. 2010 One week at Delft Institute of Applied Mathematics, Technical University Delft (The Nether- lands). • Oct. 2010 – Dec. 2010 Three months at Mathematical Analysis Department, University of Zaragoza (Spain). • Nov. 2010 One week at Mathematics Department, University of Buenos Aires (Argentina). • Jun. 2011 One week at Mathematics Department, University of Buenos Aires (Argentina). • Jun. 2011 One week at Mathematical Analysis Department, University of La Laguna (Spain). • Nov. 2011 One week at Mathematical Analysis Department, University of La Laguna (Spain). • Nov. 2011 One week at Department of Mathematics, Autonomous University of Madrid (Spain). • Feb. 2012 One week at Mathematical Analysis Department, University of Zaragoza (Spain). • Jun. 2012 One week at Mathematical Analysis Department, University of M´alaga (Spain). • Jun. 2012 One week at Mathematical Departments of Universit`adegli Studi di Napoli “Federico II” and Universit`adegli Studi di Napoli “Parthenope” (Italy). • Dec. 2012 One week at Department of Mathematics and Computation, University of La Rioja (Spain). • Jan. 2013 One week at Department of Mathematics, Autonomous University of Madrid (Spain).

L. Assistance to the courses and conferences given at:

(1) Annual Meetings of Argentinean Mathematical Union of 2003, 2004, 2005 and 2009, Argentina. (2) IMPA Summer School 2005, at Rio de Janeiro, Brazil. (3) Second Encounter of Differential Geometry 2005, at La Falda, Argentina. (4) Second International Encounter of nonlinear PDEs 2005, at Buenos Aires, Argentina. (5) Numerical Methods for PDE 2005, at Buenos Aires, Argentina. (6) First School of Mathematical Models and Economical Behavior 2005, at Merlo, San Luis, Argentina. (7) Recent developments in Real and Harmonic Analysis – Meeting in Honor of Carlos Segovia 2005, at Buenos Aires, Argentina. (8) Third Summer School of PhD Program in Applied Sciences and Mathematical Engineering 2006, at University of Concepci´on, Chile. (9) Harmonic Analysis and Applications – 8th National Encounter of Analysts “A.P. Calder´on”2006, at Merlo, San Luis, Argentina. (10) Harmonic Analysis and Applications 2007, at , Spain. (11) X Real and Complex Analysis Meetings – X EARCO 2007, at Palma de Mallorca, Spain. (12) SMI Summer School 2007, at Perugia, Italy. (13) SIMUMAT Summer School 2007, at Castro Urdiales, Spain. (14) International Multidisciplinary Workshop on Stochastic Modeling 2007, University of Seville, Spain. (15) III International Course of Mathematical Analysis in Andalucia, 2007, at La R´abida, Spain. (16) Harmonic Analysis and Orthogonal Systems 2007, at Miraflores de la Sierra, Spain. (17) Topics in PDEs and Applications 2008, at Granada, Spain. (18) CIMPA School “Real analysis and applications” 2008, at La Falda, Argentina. (19) 8th International Conference on Harmonic Analysis and PDE 2008, at El Escorial, Spain. (20) Bio–Math Summer School and Workshop 2008 – Stochastic Differential Equation Models with Appli- cations to the Insulin–Glucose System and Neuronal Modeling, at Middelfart, Denmark. (21) SPDEs: Computations and Applications 2008, at ICMS, Edinburgh, United Kingdom. (22) IV International Symposium on Nonlinear PDEs and Free Boundary Problems 2009, at Mar del Plata, Argentina. (23) XI Real and Complex Analysis Meetings – XI EARCO 2009, at Chinch´on, Spain. (24) INdAM Intensive Period “Geometric properties of nonlinear local and nonlocal problems” 2009, at Pavia, Italy. CURRICULUM VITAE OF PABLO RAUL´ STINGA 5

(25) Phase Variations 2009, at Pavia, Italy. (26) C.I.M.E. Summer Course “Regularity estimates for nonlinear elliptic and parabolic problems” 2009, at Cetraro, Italy. (27) XII Real and Complex Analysis Meetings – XII EARCO 2010, at Haro, Spain. (28) Harmonic Analysis and Orthogonal Systems IV 2010, at Bedlewo, Poland. (29) V Research Meeting on Approximation Theory 2010, at Benasque, Spain. (30) XIII Real and Complex Analysis Meetings – XIII EARCO 2011, at Zarautz, Spain. (31) Fabes Lectures 2011 – Conference on Real Analysis and PDEs, at Buenos Aires, Argentina. (32) 22nd International Workshop on Operator Theory and its Applications – IWOTA 2011, at Sevilla, Spain. (33) Workshop of Young Researchers in Mathematics 2011, at Universidad Complutense de Madrid, Spain. (34) VI Research Meeting on Approximation Theory 2011, at Canfranc, Spain. (35) 9th International Conference on Harmonic Analysis and Partial Differential Equations El Escorial 2012, at El Escorial, Spain. (36) Summer School 2012 on Nonlocal Operators, at Bielefeld University, Germany. (37) Nonlocal Operators: Analysis, Probability, Geometry and Applications 2012, at ZiF Bielefeld, Ger- many. (38) IV Congreso Latinoamericano de Matem´aticosCLAM 2012, at National University of C´ordoba, Ar- gentina. (39) Special Functions, Partial Differential Equations and Harmonic Analysis, a conference in honor of Calixto P. Calder´on2012, at Roosevelt University, Chicago, USA.

M. Other scientific activities • Reviewer for AMS Mathematical Reviews (from 2011). • Referee for: Analysis & PDE, Positivity, Journal de Math´ematiquesPures et Appliqu´ees,Annales de l’Institut Henri Poincar´e(C) Analyse Non Lin´eaire,Electronic Journal of Differential Equations.

N. Languages • English: fluent speaking, reading and writing. • Italian: perfect speaking, reading and writing. Certified by Certificazione Internazionale PLIDA from Universit`adella Tuscia di Viterbo and Societ`aDante Alighieri (Italy). • Spanish: mother tongue.