CV and List of Publications

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
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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
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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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