Curriculum Vitae of Sandra Cerrai

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1 Curriculum Vitae of Sandra Cerrai Born: October 3, 1969 Citizenship: Italian Civil status: married and two sons, David (07/19/2002) and Jacopo (09/14/2005) Languages: Fluent in English, some knowledge of French, Italian maternal language. Education Dicember 1998 PhD in Mathematics Scuola Normale Superiore of Pisa (70/70 cum laude) November 1992 MSc in Mathematics University of Pisa (110/110 cum laude) June 1988 High School Diploma (classics curriculum) Liceo Classico of Pisa (60/60). Employment history presently Associate Professor University of Maryland presently (on leave) Professore Associato (Associate Professor) University of Florence 7/ /2001 Ricercatore (Assistant Professor) University of Florence. 1

2 Awards 1. NSF Research Grant DMS ( ) Asymptotic Problems for Stochastic Partial Differential Equations (Principal Investigator). 2. Grant from the TMR network Viscosity solutions and applications, local coordinator in Paris Prof. P.L. Lions, April-May Perfezionamento fellowship at the Scuola Normale Superiore of Pisa, 01/ /1995. Professional service 1. Department, Salary Committee 2009, Policy Committee 2009-present, Hiring Committee Panelist for the National Science Foundation. 3. Mathematical community, Associate Editor of Journal of Theoretical Probability, August 2009-present. Organization of workshops and seminars 1. Organizer of the Invited Session on Large deviations for SPDE at the XXXV International Conference on Stochastic Processes and their Applications (Mexico, June 2011), sponsored by the Bernoulli Society for Mathematical Statistics and Probability and the Institute of Mathematical Statistics. 2. Workshop on Stochastic Partial Differential Equations, Centro de Giorgi, Pisa 3-7 aprile 2006, co-organizer. 2

3 Publications Book 1. Sandra Cerrai, Second order PDE s in finite and infinite dimensions. A probabilistic approach, x+330 pp. Lecture Notes in Mathematics 1762 (2001), Springer Verlag. Articles in research journals 2. Sandra Cerrai, Mark Freidlin: Approximation of quasi-potentials and exit problems for multidimensional RDE s with noise, Transactions of the AMS 363 (2011), pp Sandra Cerrai, Mark Freidlin: Fast transport asymptotics for stochastic RDE s with boundary noise, Annals of Probability 39 (2011), pp Sandra Cerrai: Normal deviations from the averaged motion for some reaction-diffusion equation with fast oscillating perturbation, Journal de Matématiques Pures et Appliqués 91 (2009), pp Sandra Cerrai: A Khasminskii type averaging principle for stochastic reaction-diffusion equations, Annals of Applied Probability 19 (2009), pp Sandra Cerrai, Mark Freidlin: Averaging principle for a class of SPDE s, Probability Theory and Related Fields 144 (2009), pp Sandra Cerrai, Philippe Clément: Schauder estimates for a degenerate second order elliptic operator on a cube, Journal of Differential Equations 242 (2007), pp Sandra Cerrai, Mark Freidlin: Smoluchowski-Kramers approximation for a general class of SPDE s, Journal of Evolution Equations 6 (2006), pp Sandra Cerrai, Mark Freidlin: On the Smoluchowski-Kramers approximation for a system with an infinite number of degrees of freedom, Probability Theory and Related Fields 135 (2006), pp

4 10. Sandra Cerrai: Stabilization by noise for a class of stochastic reactiondiffusion equations, Probability Theory and Related Fields 133 (2005), pp Sandra Cerrai, Philippe Clément: Erratum to Schauder estimates for a class of second order elliptic operators on a cube, Bulletin des Sciences Mathématiques 129 (2005), p Sandra Cerrai, Michael Röckner: Large deviations for invariant measures of stochastic reaction-diffusion systems with multiplicative noise and non-lipschitz reaction term, Annales de l Institut Henri Poincaré (Probabilités et Statistiques) 41 (2005), pp Sandra Cerrai, Philippe Clément: Well-posedness of the martingale problem for some degenerate diffusion processes occurring in dynamics of populations, Bulletin des Sciences Mathématiques 128 (2004), pp Sandra Cerrai, Michael Röckner: Large deviations for stochastic reaction-diffusion systems with multiplicative noise and non-lipschitz reaction term, Annals of Probability 32 (2004), pp Sandra Cerrai, Michael Röckner: Large deviations for invariant measures of general stochastic reaction-diffusion systems, Comptes Rendus Acad. Sci. Paris S. I Math. 337 (2003), pp Sandra Cerrai: Stochastic reaction-diffusion systems with multiplicative noise and non-lipschitz reaction term, Probability Theory and Related Fields 125 (2003), pp Sandra Cerrai, Philippe Clément: Schauder estimates for a class of second order elliptic operators on a cube, Bulletin des Sciences Mathématiques 217 (2003), pp Sandra Cerrai, Philippe Clément: On a class of degenerate elliptic operators arising from the Fleming-Viot processes, Journal of Evolution Equations 1 (2001), pp Sandra Cerrai: Stationary Hamilton-Jacobi equations in Hilbert spaces and applications to a stochastic optimal control problem, SIAM Journal on Control and Optimization 40 (2001), pp

5 20. Sandra Cerrai: Optimal control problems for stochastic reaction-diffusion systems with non Lipschitz coefficients, SIAM Journal on Control and Optimization 39 (2001), pp Sandra Cerrai: Analytic semigroups and degenerate elliptic operators with unbounded coefficients: a probabilistic approach, Journal of Differential Equations 166 (2000), pp Sandra Cerrai: Ergodicity for stochastic reaction-diffusion systems with polynomial coefficients, Stochastics and Stochastics Reports 67 (1999), pp Sandra Cerrai: Differentiability of Markov semigroup for stochastic reactiondiffusion equations and applications to control, Stochastic Processes and their Applications 83 (1999) pp Sandra Cerrai: Smoothing properties of transition semigroups relative to SDEs with value in Banach spaces, Probability Theory and Related Fields 113 (1999) pp Sandra Cerrai: Kolmogorov equations in Hilbert spaces with non smooth coefficients, Communications in Applied Analysis 2 (1998) pp Sandra Cerrai: Differentiability with respect to initial datum for solutions of SPDE s with no Fréchet differentiable drift term, Communications in Applied Analysis 2 (1998) pp Sandra Cerrai: Some results for second order elliptic operators having unbounded coefficients, Differential and Integral Equations 11 (1998) pp Sandra Cerrai: Invariant measures for a class of SDE s with drift term having polynomial growth, Dynamic Systems and Applications 5 (1996), Sandra Cerrai: Elliptic and parabolic equations in R n with coefficients having polynomial growth, Communications in Partial Differential Equations 21 (1996) Sandra Cerrai, Fausto Gozzi: Strong solutions of Cauchy problems associated to weakly continuous semigroups, Differential and Integral Equations 8 (1995)

6 31. Sandra Cerrai: Weakly continuous semigroups in the space of functions with polynomial growth, Dynamic Systems and Applications 4 (1995) Sandra Cerrai: A Hille Yosida theorem for weakly continuous semigroups, Semigroup Forum 49 (1994) Articles in volumes (refereed) 33. Sandra Cerrai: Ergodic properties of reaction-diffusion equations perturbed by a degenerate multiplicative noise, Operator Theory: Advances and Applications vol. 168 (2006), Birkhäuser Verlag Basel, pp Sandra Cerrai: Asymptotic behavior of systems of SPDE s with multiplicative noise, Stochastic Partial Differential Equations and Applications VII, Lecture Notes in Pure and Applied Mathematics vol. 245 (2006), Chapman and Hall/CRC Press, pp Sandra Cerrai, Classical solutions for Kolmogorov equations in Hilbert spaces, Third Seminar on Stochastic Analysis, Random Fields and Applications, Ascona, Progress in Probability 52, Birkhäuser Verlag, (2002), pp Sandra Cerrai, A generalization of the Bismut-Elworthy formula, Evolution Equations and their Applications in Physical and Life Sciences, edited by G. Lumer and L. Wiess, Lecture Notes in Pure and Applied Mathematics Vol. 215, Marcel Dekker (2000). Preprints 37. Sandra Cerrai: Averaging principle for systems of RDEs with polynomial nonlinearities perturbed by multiplicative noise, submitted to Siam Journal of Mathematical Analysis. 38. Sandra Cerrai, Mark Freidlin: Small mass asymptotics for a charged particle in magnetic field and long-time influence of small perturbations, submitted to Journal of Statistical Physics. 39. Sandra Cerrai, Giuseppe Da Prato: Schauder estimates for Kolmogorov equations in Banach spaces associated with stochastic reaction-diffusion equations, submitted to Journal of Functional Analysis. 6

7 Theses Sandra Cerrai, Transition semigroups corresponding to stochastic dynamical systems with unbounded coefficients, PhD Thesis, advisor Prof. Giuseppe Da Prato, Scuola Normale Superiore, Pisa, Sandra Cerrai, Equazioni paraboliche in dimensione infinita (Parabolic equations in infinite dimensions), MSc Thesis, advisor Prof. Giuseppe Da Prato, University of Pisa, Conference and workshop presentations Parabolic equations with unbounded coefficients, Workshop on PDE s methods in Control, Shape Optimization and Stochastic Modelling, Pisa Scuola Normale Superiore December 8-10, Regolarità per le soluzioni dell equazione di Kolmogorov (Regularity of the solutions of Kolmogorov equations), Convegno su equazioni di evoluzione e applicazioni alla teoria del trasporto e alla biologia, Roma February 23-25, Elliptic and parabolic equations with polynomial coefficients in R n, Conference on nonlinear parabolic problems, Levico Terme June 11-16, Elliptic and parabolic equations with coefficients having polynomial growth, Dynamical systems and applications of stochastic differential equations, Pisa Scuola Normale Superiore June 29-30, Equazioni ellittiche e paraboliche in R n con coefficienti aventi crescita polinomiale (Elliptic and parabolic equations in R n with coefficients having polynomial growth), XV Congresso dell Unione Matematica Italiana, Padova September 11-16,

8 Schauder estimates for Kolmogorov equations with unbounded coefficients, 11th Winter school on stochastic processes, Jena March 17-23, Invariant measures for systems with coefficients having polynomial growth, Workshop on deterministic and stochastic evolutionary systems, Pisa Scuola Normale Superiore July 16-17, Smoothing properties for transition semigroups relative to stochastic PDEs with unbounded coefficients, Workshop on deterministic and stochastic evolutionary systems, Pisa Scuola Normale Superiore, July 16-18, Smoothing properties for transition semigroups relative to stochastic PDEs with non Lipschitz drift Term, Workshop on infinite dimensional stochastic systems, Praga, September 8-12, Regularizing properties for some stochastic reaction-diffusion equations, Workshop on stochastic partial differential equations, Berkeley, September 15-19, Proprietà di regolarizzazione per il semigruppo di transizione relativo ad alcune equazioni di reazione-diffusione stocastiche (Regularizing properties for the transition semigroup corresponding to some stochastic reaction-diffusion equations), Convegno su equazioni di evoluzione e applicazioni alla teoria del trasporto e alla biologia, Montecatini Terme February 19-21, Invariant measures for stochastic reaction-diffusion systems, III Ciclo CIME Stochastic PDE s and Kolmogorov equations in infinite dimensions, Cetraro, August 24-September 1,

9 Ergodicity for stochastic reaction-diffusion systems with unbounded coefficients, Sixth international conference on evolution equations and their applications in physical and life sciences, Bad Herrenalb, September 14-19, Probabilistic methods in the study of analytic semigroups generated by second order degenerate elliptic operators, Optimal regularity in elliptic, hypoelliptic and parabolic problems, Levico Terme October 6-10, Sistemi di reazione diffusione stocastici: proprietà di regolarizzazione (Stochastic reaction-diffusion systems: regularizing properties), XVI Congresso Unione Matematica Italiana, Napoli September 13-18, Stationary Hamilton-Jacobi equations in Hilbert spaces and applications to a stochastic optimal control problem, Third seminar on stochastic analysis, random fields and applications, Ascona, September 20-24, Classical solutions for Kolmogorov equations in infinite dimensions, Conference on Stochastic partial differential equations and applications, Levico Terme, January 10-15, On a class of degenerate elliptic operators arising from the Fleming-Viot processes International Conference on Viscosity Solutions and Applications, Analysis and Control of Deterministic and Stochastic Evolution Equations, Bressanone, July 3-7, Degenerate elliptic operators arising from dynamic of populations Workshop on Infinite Dimensional Stochastic Systems, Praga, September 11-15,

10 Optimal control for stochastic Ginzburg-Landau systems Mini-Symposium on Stochastic reaction diffusion equations, Loughborough June 15-16, Kolmogorov equations in Hilbert spaces Workshop on Stochastic Partial Differential equations, Warwick July 16-27, Large deviations for a class of stochastic reaction-diffusion systems with multiplicative noise Stochastic evolution equations and applications, Oberwolfach October 1-6, Stochastic reaction-diffusion systems with multiplicative noise Conference on stochastic partial differential equations and applications- VI, Levico Terme (Trento), January 7-12, Large deviations for a class of SPDE s with multiplicative noise First joint international meeting, American Mathematical Society-Unione Matematica Italiana, Pisa, June 12-16, Large deviations for a general class of SPDE s Workshop on stochastic partial differential equations and related topics, Warwick, August 4-15, Some elliptic degenerate equations arising in population dynamics Two days on Kolmogorov equations, Centro De Giorgi, Pisa, October 17-18, Large deviations for the invariant measures of a class of stochastic reaction-diffusion systems International Conference on Stochastic Partial Differential Equations and Applications-VII, Levico Terme (Trento), January 4-10,

11 Ergodicity for some stochastic reaction-diffusion equations IFIP 7.2 Boundary Control and Optimization, Scuola Normale Superiore- Centro De Giorgi, Pisa, February 26-28, Sull approssimazione di Kramers-Smolukowski per un sistema con un numero infinito di gradi di libertà (On the Kramers-Smolukowski approximations for a system with an infinite number of degrees of freedom), Incontro su Equazioni di Kolmogorov, Parma November 26-27, On the martingale problem for a class of degenerate diffusion processes arising from the dynamics of populations, Workshop on Partial Differential Equations and Functional Analysis, Delft, November 29-December 1, On the Kramers-Smolukowski approximation for a class of SPDE s, Conference on Stochastic Partial Differential Equations and Random Media: from Theory to Applications I, Zif (Zentrum für Interdisziplinäre Forschung) Bielefeld April 4-8, On the ergodic properties of some classes of spde s, Workshop on Stochastic Partial Differential Equations, Centro de Giorgi, Pisa April 3-7, The Smoluchowski-Kramers approximation for a general class of SPDE s, Workshop on Hydrodynamic limits and Particle Systems, Centro de Giorgi, Pisa June 5-9, Averaging principle for a class of SPDE s, Workshop on Kolmogorov equations, Parma November 1-3, Averaging principle for some stochastic partial differential equations One day on Kolmogorov equations, Centro De Giorgi, Pisa March

12 On the averaging principle for a general class of SPDE s, Conference on stochastic dynamics, Paris June Fluctuations in SPDE s with averaging, Joint international meeting UMI-DMV, Perugia June Fluctuations in SPDE s with averaging, Workshop on stochastic partial differential equations, Mittag-Leffler Institut, Djursholm, September On an averaging result for a class of SPDE s, Conference on Stochastic Partial Differential Equations and Applications- VIII, Levico Terme, January Fast diffusion asymptotics for stochastic reaction-diffusion equations with boundary noise, Workshop on New scaling limits and other recent developments in probability, Warwick, March 31- April 4, Normal deviations from the averaged motion for some reactiondiffusion equation with fast oscillating perturbation, Sixth Seminar on Stochastic Analysis, Random Fields and Applications, Ascona May 19-23, Fast transport asymptotics for SPDE s with noise acting on the boundary, Opening Workshop, SAMSI program on Stochastic Dynamics, Research Triangle Park, NC, August 30-September 2, On some averaging results for SPDE s, SIAM Conference on analysis of PDEs, Miami, December 7-10, Approximation of quasi-potentials and exit problems for multidimensional RDEs, Workshopon SPDEs, Isaac Newton Institute for Mathematical Sciences, January

13 Invited talks Semigruppi debolmente continui e loro applicazioni alle equazioni differenziali stocastiche (Weakly continuous semigroups and their applications to stochastic differential equations), Politecnico of Torino, May Asymptotic behavior for a class of SDE s with drift term having polynomial growth, University of Trento, October Schauder Estimates and asymptotic behaviour for elliptic operator with unbounded coefficients, University of Parma, June Elliptic equations with unbounded coefficients, University of Southern California (Los Angeles), Center for Applied Mathematical Sciences, September Generation of analytic semigroups by degenerate elliptic operators, University of Paris 13, March Infinite dimensional Hamilton-Jacobi equations with non Lipschitz coefficients, University of Paris 9, May Hamilton-Jacobi equations with polynomial nonlinearities and applications to stochastic control, University of Delft, May Equazioni di Hamilton-Jacobi in spazi di Hilbert, University of Roma Tor Vergata, December

14 Degenerate elliptic operators arising from the Fleming- Viot processes, University of Bonn, March On a class of degenerate elliptic operators arising from the Fleming-Viot processes, University of Delft, April Equazioni paraboliche con coefficienti non limitati (Parabolic equations with unbounded coefficients), University of Trento, June Problemi di controllo ottimo a frontiera infinita per sistemi di reazione-diffusione stocastici (Infinite horizon optimal control problems for stochastic reaction-diffusion systems), University of Trento, March Finite horizon control problems for a class of stochastic Ginzburg-Landau systems, University of Geneva, April Infinite horizon control problems for stochastic Ginzburg- Landau systems, University of Delft, May Large deviations estimates for stochastic Ginzburg-Landau systems with multiplicative noise, University of Delft, November On the Smolukowski-Kramers approximation for a class of SPDE s, École Polytechnique Fédérale de Lausanne, March On the averaging principle for some SPDE s Mathematics Institute, University of Warwick, February

15 On some asymptotic problems for SPDE s Center for Dynamics and Geometry, Department of Mathematics, Penn State University, February On some asymptotic problems for SPDE s Department of Mathematics, University of Maryland at College Park, February A Khasminskii type averging result for SPDE s Department of Mathematics, University of Maryland at College Park, September On the averaging principle for stochastic partial differential equations Department of Applied Mathematics, Brown University, March Research periods abroad Center for Applied Mathematical Sciences, University of Southern California (Los Angeles), September Invited by Prof. B.Rozovsky. Laboratoire Analyse, Géométrie et Applications, University of Paris 13, March Invited by Prof. F. Russo. Centre de Recherche de Mathématiques de la Décision (Ceremade), University of Paris 9, April-May Department of Applied Mathematics, Delft University of Technology, May 1999, April 2000, May 2001, November 2001, September Invited by Prof. Ph. Clément. Fakultät für Mathematik, Università di Bielefeld, March Invited by Prof. M. Roeckner. 15

16 Mathematics Research Centre, University of Warwick, July-August Invited by Prof. D.K. Elworthy during the Warwick Sumposium on Stochastic Differential Equations and Related Topics, October August Institut Mittag-Leffler, Djursholm Sweden, September Invited by Professors Oksendal, Sanz-Solé and Roeckner in the semester on Stochastic Partial Differential Equations. Isaac Newton Institute for Mathematical Sciences, Cambridge United Kingdom, June-July Invited by Professors Brzezniak, Hairer and Roeckner in the semester on Stochastic Partial Differential Equations. Referee activity I am associate editor of the Journal of Theoretical Probability. Moreover, I have been referee of research articles for the following journals: Annals of Probability, Applied Mathematics and Optimization, Bulletin of the Australian Mathematical Society, Discrete and Continuous Dynamical Systems, Journal of Differential and Integral Equations, Journal of Evolution Equations, Journal of Mathematical Physics, Journal of Nonlinear Analysis, Journal of Theoretical Probability, Potential Theory, Probability Theory and Related Fields, SIAM Journal of Mathematical Analysis, Stochastic and Dynamics, Stochastic Processes and their Applications. 16