CURRICULUM VITAE AND LIST OF PUBLICATIONS GIANLUCA CRIPPA Associate Professor in Analysis — Departement Mathematik und Informatik — Universit¨ at Basel Born in Lecco (Italy), on April 30, 1981. Citizenship: Italian. Personal status: single. Education • Fall 2000: Winner of a four-years fellowship at the Scuola Normale Superiore di Pisa. • Fall 2000 – Summer 2004: Undergraduate program in Mathematics, jointly at the Scuola Normale Superiore and the University of Pisa. • Summer 2004: Laurea in Matematica (equivalent to MSc) with distinction at the University of Pisa. Thesis directed by Luigi Ambrosio. • Fall 2004: Winner of a PhD fellowship in Mathematics at the Scuola Normale Superiore di Pisa. • Fall 2004 – Fall 2007: PhD studies jointly at the Scuola Normale Superiore di Pisa and the Institute for Mathematics of the University of Z¨ urich (co-supervision). • Spring 2005: Diploma di Licenza with distinction at the Scuola Normale Superiore di Pisa. This is the final degree for the undergraduate program at the Scuola Normale Superiore di Pisa. • Spring 2008: Award of the PhD title with thesis directed by Luigi Ambrosio and Camillo De Lellis. “Diploma di Perfezionamento in Matematica” with distinction (Pisa) and title of “Doctor scientiarum naturalium” with distinction and a prize (Z¨ urich). Academic Positions and Offers • • • • • Fall 2007 – Fall 2011: Assistant Professor (Ricercatore Universitario, tenured), Parma, IT. Spring 2011: Shortlisted for a Full Professorship (W3) at RWTH Aachen, DE. Fall 2011 – Fall 2012: Assistant Professor (with tenure track) in Analysis, Basel. Spring 2012: Offer of a Full Professorship (W3) from Mainz, DE. Declined. Since Fall 2012: Extraordinarius (tenured Associate Professor) in Analysis, Basel. Research Projects • • • • • PRIN 2004, PRIN 2006, PRIN 2008 (Luigi Ambrosio). PRIN 2012 (Stefano Bianchini). INdAM 2005 (Benedetto Piccoli). GNAMPA 2008 (coordinator), GNAMPA 2009 (Simona Fornaro). ERC ConLaws 2009 (Stefano Bianchini). SNF 200021 140232, “Continuity equations with non smooth velocity: fluid dynamics and further applications”, 01.04.2012 – 30.09.2014, ca. CHF 150’000 (coordinator). • SNF 200020 156112, “Continuity equations with non smooth velocity: quantitative estimates and applications to nonlinear problems”, 01.10.2014 – 30.09.2017, ca. CHF 250’000 (coordinator). Date: September 27, 2014. Institutional, Scientific and Didactic Activities • Current workgroup at the University of Basel: Anna Bohun (PhD student, since Oct. 2011), Silvia Ligabue (PhD student, since Oct. 2014). Past member: Dr. Stefano Spirito (PostDoc, Sept. 2012–Aug. 2014). • BSc and MSc theses supervised: in Parma: Marcello Carioni (BSc, Dec. 2009), Alessandra De Gregorio (BSc, Dec. 2010), Michele Terribilini (MSc, Apr. 2011), Silvia Ligabue (BSc, Oct. 2011), Marcello Carioni (MSc, Apr. 2012); in Basel: Irina Oberlin (MSc, Feb. 2014), Stephan Heule (MSc, Feb. 2014), Silvia Ligabue (MSc Uni Pisa, co-supervision Sept. 2014). • Organization of conferences and schools: – “Microlocal Analysis and Applications to PDEs”, Pisa, November 2006. – “Intensive Research Month on Hyperbolic Conservation Laws and Fluid Dynamics”, Parma, February 2010. – “Nonlinear Problems in PDEs”, Parma, April – June 2010. – “Nonlinear Hyperbolic PDEs, Dispersive and Transport Equations: Analysis and Control”, SISSA, Trieste, May – July 2011. – “HYP2012, 14th International Conference on Hyperbolic Problems: Theory, Numerics, Applications”, Padova, June 25 – 29, 2012. – “Basel Junior Symposium in Analysis”, Basel, February 12 – 14, 2013. – “10th Meeting on Hyperbolic Conservation Laws and Fluid Dynamics”, L’Aquila, July 11 – 12, 2013. – “Two days on Hyperbolic PDEs, Geometric Measure Theory and Optimal Transport”, SISSA, Trieste, October 28 – 29, 2013. – “Summer School on Geometric Measure Theory and Geometric Analysis”, Basel, June 23 – 27 and July 14 – 18, 2014. • Editorial and referee activities: Differential and Integral Equations: member of Editorial Board since January 2014. Measure theory (open access book series edited by De Gruyter): series editor since April 2014. — Proceedings of the Seventh Meeting on Hyperbolic Conservation Laws and Fluid Dynamics: Recent Results and Research Perspectives. Rivista di Matematica della Universit` a di Parma, 2010. Proceedings of the Intensive Research Month on Hyperbolic Conservation Laws and Fluid Dynamics. Rivista di Matematica della Universit`a di Parma, 2012. HCDTE Lecture Notes. Part I + II. AIMS Book Series on Applied Mathematics, 2013 and 2014. — Referee for several journals, book series, research proposals, PhD theses. Conferences and Visiting Activities • Visits for collaborations to the following institutions: – Italy: Padova, Pavia, CNR Pavia, Pisa, Scuola Normale Superiore di Pisa, Roma La Sapienza, Trento, SISSA Trieste; ´ – France: Ecole Normale Sup´erieure de Paris, Laboratoire J.-L. Lions (Paris VI), Paris-Est ´ Marne-la-Vall´ee, Paris-Sud Orsay, Ecole Normale Sup´erieure de Lyon, Besan¸con, Brest; – Germany: Institute for Applied Mathematics (Bonn); – Switzerland: Institute for Mathematics (Z¨ urich); – Spain: Universidad Complutense de Madrid; – UK: OxPDE - Oxford Centre for Nonlinear PDE; – USA: Northwestern Univ., Division of Applied Math. (Brown Univ.), CSCAMM (Maryland). • More than 60 conferences, talks, colloquia and research courses given, mostly on invitation. • More than 70 schools and conferences attended. List of Publications The papers below are available for download from the webpages http://www.math.unibas.ch/crippa and http://cvgmt.sns.it/people/crippa A full list of publications is available for download from the webpage http://www.math.unibas.ch/crippa Peer-reviewed articles. • Luigi Ambrosio, Gianluca Crippa & Stefania Maniglia: Traces and fine properties of a BD class of vector fields and applications. Ann. Fac. Sci. Toulouse Math. (6) 14 (2005), no. 4, 527–561. • Gianluca Crippa & Camillo De Lellis: Oscillatory solutions to transport equations. Indiana Univ. Math. J. 55 (2006), no. 1, 1–13. • Ferruccio Colombini, Gianluca Crippa & Jeffrey Rauch: A note on two-dimensional transport with bounded divergence. Comm. Partial Differential Equations 31 (2006), no. 7, 1109–1115. • Franc ¸ ois Bouchut & Gianluca Crippa: Uniqueness, renormalization and smooth approximations for linear transport equations. SIAM J. Math. Anal. 38 (2006), no. 4, 1316–1328. • Gianluca Crippa & Camillo De Lellis: Estimates and regularity results for the DiPerna– Lions flow. J. Reine Angew. Math. 616 (2008), 15–46. • Luigi Ambrosio, Gianluca Crippa & Philippe G. LeFloch: Leaf superposition property for integer rectifiable currents. Netw. Heterog. Media 3 (2008), no. 1, 85–95. ´ Jimenez & Aldo Pratelli: Optimum and equilibrium in a trans• Gianluca Crippa, Chloe port problem with queue penalization effect. Advances in Calculus of Variations 2 (2009), no. 3, 207–246. • Luigi Ambrosio, Gianluca Crippa, Alessio Figalli & Laura V. Spinolo: Some new wellposedness results for continuity and transport equations, and applications to the chromatography system. SIAM J. Math. Anal. 41 (2009), no. 5, 1890–1920. • Gianluca Crippa: Lagrangian flows and the one-dimensional Peano phenomenon for ODEs. Journal of Differential Equations 250 (2011), no. 7, 3135–3149. • Emilio Acerbi, Gianluca Crippa & Domenico Mucci: A variational problem for multifunctions with interaction between leaves. ESAIM Control Optim. Calc. Var. 18 (2012), no. 4, 1178–1206. ´cureux-Mercier: Existence and uniqueness of measure so• Gianluca Crippa & Magali Le lutions for a system of continuity equations with non-local flow. Nonlinear Differential Equations and Applications NoDEA 20 (2013), no. 3, 523–537. • Franc ¸ ois Bouchut & Gianluca Crippa: Lagrangian flows for vector fields with gradient given by a singular integral. J. Hyper. Differential Equations 10 (2013), no. 2, 235–282. • Giovanni Alberti, Stefano Bianchini & Gianluca Crippa: Structure of level sets and Sard-type properties of Lipschitz maps: results and counterexamples. Annali della Scuola Normale Superiore di Pisa Classe di Scienze (5) XII (2013), 863–902. • Giovanni Alberti, Stefano Bianchini & Gianluca Crippa: A uniqueness result for the continuity equation in two dimensions. Journal of the European Mathematical Society (JEMS) 16 (2014), Issue 2, 201–234. • Giovanni Alberti, Stefano Bianchini & Gianluca Crippa: On the Lp differentiability of certain classes of functions. Revista Matem´atica Iberoamericana 30 (2014), no. 1, 349–367. • Gianluca Crippa, Carlotta Donadello & Laura V. Spinolo: Initial-boundary Value Problems for Continuity Equations with BV Coefficients. Journal de Math´ematiques Pures et Appliqu´ees 102 (2014). 79–98. • Giovanni Alberti, Gianluca Crippa and Anna L. Mazzucato: Exponential self-similar mixing and loss of regularity for continuity equations. Comptes Rendus Mathematique, in press. Review articles – Proceedings (all peer-reviewed). • Gianluca Crippa & Camillo De Lellis: Regularity and compactness for the DiPerna–Lions flow. Hyperbolic Problems: Theory, Numerics, Applications. Proceedings of the International Conference on Hyperbolic Problems “HYP2006”, held at the Ecole Normale Sup´erieure, Lyon, July 17–21, 2006. pp. 423–430. Edited by S. Benzoni-Gavage, D. Serre. Springer Verlag, 2008. • Gianluca Crippa: The ordinary differential equation with non-Lipschitz vector fields. Boll. Unione Mat. Ital. (9) 1 (2008), no. 2, 333–348. ´ Jimenez & Aldo Pratelli: A transport problem with queue pe• Gianluca Crippa, Chloe nalization effect. In “Singularities in nonlinear evolution phenomena and applications”, 139–156, CRM Series 9, Ed. Norm., Pisa, 2009. Edited by Matteo Novaga and Giandomenico Orlandi. • Franc ¸ ois Bouchut & Gianluca Crippa: Equations de transport ` a coefficient dont le gradient est donn´e par une int´egrale singuli`ere. (French) [Transport equations with a coefficient whose ´ gradient is given by a singular integral]. S´eminaire: Equations aux D´eriv´ees Partielles. 2007– ´ ´ 2008, Exp. No. I, 15 pp., S´emin. Equ. D´eriv. Partielles, Ecole Polytech., Palaiseau, 2009. • Giovanni Alberti, Stefano Bianchini & Gianluca Crippa: Two-Dimensional Transport Equation with Hamiltonian Vector Fields. Hyperbolic Problems: Theory, Numerics and Applications. Proceedings of the International Conference on Hyperbolic Problems “HYP2008”, held at the University of Maryland, College Park, June 9–13, 2008, pp. 337–346. Edited by E. Tadmor, J.-G. Liu, A. Tzavaras. Proceedings of Symposia in Applied Mathematics, 67. American Mathematical Society, Providence, 2009. • Gianluca Crippa & Laura V. Spinolo: An overview on some results concerning the transport equation and its applications to conservation laws. Communications on Pure and Applied Analysis 9 (2010), no. 5, 1283–1293. • Giovanni Alberti, Stefano Bianchini & Gianluca Crippa: Divergence-free vector fields in R2 . Proceedings of the Fifth International Conference on Differential and Functional Differential Equations. Journal of Mathematical Sciences 170 (2010), no. 3, 283–293. Russian Version: in Sovrem. Mat. Fundam. Napravl. 35 (2010), 22–32. • Luigi Ambrosio, Gianluca Crippa, Alessio Figalli & Laura V. Spinolo: Existence and uniqueness results for the continuity equation and applications to the chromatography system. In “Nonlinear Conservation Laws and Applications”, IMA Vol. Math. Appl. 153, edited by Alberto Bressan, Gui-Qiang Chen, Marta Lewicka, and Dehua Wang. Springer 2011. • Gianluca Crippa: Ordinary Differential Equations and Singular Integrals. Hyperbolic Problems: Theory, Numerics, Applications. Proceedings of the International Conference on Hyperbolic Problems “HYP2012”, held in Padova on June 2429, 2012. Editors: Fabio Ancona, Alberto Bressan, Pierangelo Marcati, Andrea Marson. AIMS Book Series on Applied Mathematics 8 (2014), pp. 109–117. • Gianluca Crippa, Carlotta Donadello & Laura V. Spinolo: A note on the initialboundary value problem for continuity equations with rough coefficients. Hyperbolic Problems: Theory, Numerics, Applications. Proceedings of the International Conference on Hyperbolic Problems “HYP2012”, held in Padova on June 2429, 2012. Editors: Fabio Ancona, Alberto Bressan, Pierangelo Marcati, Andrea Marson. AIMS Book Series on Applied Mathematics 8 (2014), pp. 957–966. Monographs. • Gianluca Crippa: The flow associated to weakly differentiable vector fields. Theses of Scuola Normale Superiore di Pisa (New Series), 12. Edizioni della Normale, Pisa, 2009 - Distributed by Birkh¨ auser. Book contributions and Lecture notes. • Luigi Ambrosio & Gianluca Crippa: Existence, uniqueness, stability and differentiability properties of the flow associated to weakly differentiable vector fields. In “Transport equations and multi-D hyperbolic conservation laws”, 3–57, Lect. Notes Unione Mat. Ital., 5, Springer, Berlin, 2008. • Gianluca Crippa, Felix Otto & Michael Westdickenberg: Regularizing effect of nonlinearity in multidimensional scalar conservation laws. In “Transport equations and multi-D hyperbolic conservation laws”, 77–128, Lect. Notes Unione Mat. Ital., 5, Springer, Berlin, 2008. • Luigi Ambrosio & Gianluca Crippa: Continuity equations and ODE flows with non-smooth velocity. Lecture Notes of a course given at Heriot-Watt University, Edinburgh. Proceedings of the Royal Society of Edinburgh, Section A: Mathematics. In press Preprints. • Gianluca Crippa, Milton Lopes Filho, Evelyne Miot & Helena Nussenzveig Lopes: Flows of Vector Fields with Point Singularities and the Vortex-Wave System. Submitted Research Paper, 2013.
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