Curriculum Vitae
Francesco Maggi email: [email protected] webpage: http://www.ma.utexas.edu/users/maggi/
Personal information: Born August 19, 1978, in Viareggio (Italy); Italian citizen; married; one child; Languages: Italian (native), English (fluent)
Positions held: Associate professor, Department of Mathematics, UT Austin, USA, since 6/12 Professore associato (Associate prof.), U. Firenze, Italy, 12/11-6/12 Visiting scholar, Department of Mathematics-ICES, UT Austin, USA, 9/11-5/12 Ricercatore (Assistant prof.), U. Firenze, Italy, 10/05-11/11 Wissenschaftlichen Assistenten C1 (Assistant prof.) U. Duisburg-Essen, Germany, 1/05-9/05 Post-doctoral associate, MPI-MIS Leipzig, Germany, 5/04-12/04
Education, awards and others: Italian habilitation as full professor in Mathematics, 12/13 (based on my curriculum on 9/12) Italian habilitation as associate professor in Mathematics, 8/10 (based on my curriculum on 8/08) Premio Carlo Miranda 2008, Accademia di Scienze Fisiche e Matematiche di Napoli PhD in Mathematics, U. Firenze, 4/04 (enrolled 9/01) Master Degree in Mathematics, U. Firenze, 7/00 (enrolled 9/96)
Research interests and main results: My research interests are in the area of Calculus of Variations and Geometric Measure Theory, with particular emphasis on geometric and functional inequalities, geometric variational problems (like least area and isoperimetric problems), and variational problems from nonlinear elasticity, image reconstruction and phase transitions. These are the main results I have obtained, with references to the list of papers below. In 7 (joint with C. Villani), by means of mass transportation techniques we prove certain optimal Sobolev inequalities with trace terms, which validity was first conjectured by Brezis and Lieb on J. Funct. Anal. 62 (1985). In 12 (joint with S. Conti), we prove - in the context of Nonlinear Elasticity - the validity of an energy scaling law for crumpled elastic sheets that was heuristically derived by Lobkovsky, Gentges, Li, Morse and Witten on Science 270 (1995). In 14 (joint with N. Fusco and A. Pratelli), we obtain a sharp stability theorem for the Euclidean isoperimetric inequality, a result first conjectured by Hall in Crelles J. 428 (1992). In 20 (joint with A. Figalli and A. Pratelli), by exploiting optimal transport theory, we prove a sharp stability theorem for the Wulff inequality, with effective constants. In 23 (joint with A. Figalli) we obtain some convexity results for liquid drops and crystals with small mass, thus answering some questions originally posed by Almgrem and Taylor. In 32-33 (joint with F. Cagnetti, M. Colombo, and G. de Philippis), we introduce a measure-theoretic notion of connectedness and we address the characterization of rigidity equality cases in Ehrhard’s inequality for Gaussian perimeter and in Steiner’s inequality for classical perimeter, thus providing a complete solution to the rigidity problem introduced by Chlebík, Cianchi, and Fusco on Ann. Math. 162 (2005). In 33 (joint with G. de Philippis) we prove a regularity theorem for free boundaries in anisotropic capillarity problems, thus showing the a.e. validity of (the anisotropic version of) Young’s law; in the anisotropic case -- where tools like monotonicty formulas, epiperimetric inequalities, and good dimensional estimates on interior singularities are not available -- this result is new even in dimension three, and unifies previous results (dealing with special situations, and limited to the isotropic case) by Taylor, Caffarelli and Friedman, and Gruter and Jost.
Collaborators: Filippo Cagnetti, Eric Carlen, Marco Caroccia, Andrea Cianchi, Marco Cicalese, Maria Colombo, Sergio Conti, Guido de Philippis, Daniel Faraco, Alessio Figalli, Irene Fonseca, Nicola Fusco, Michele Gori, Gian Paolo Leonardi, Giovanni Leoni, Paolo Marcellini, Vincent Millot, Massimiliano Morini, Stefan Mueller, Marcello Ponsiglione, Aldo Pratelli, Cédric Villani.
Papers in preparation: 38 On the convergence of planar unit area minimizing clusters with large number of chambers to honeycomb tilings (with M. Caroccia) 37 On equilibrium shapes of perturbed minimizing clusters and related global stability inequalities (with M. Cicalese and G. P. Leonardi), in preparation 36 Quantitative improvements of the Brunn-Minkowski and Riesz inequalities and applications to the shape of droplets in non-local phase transitions (with E. Carlen), in preparation. 35 The rigidity problem for Steiner’s perimeter inequalities in higher codimension (with F. Cagnetti, M. Colombo, G. De Philippis). 34 Isoperimetry and stability properties of balls with respect to non-local energies (with A. Figalli, N. Fusco, V. Millot, M. Morini)
Papers accepted for publication or in preprint form: 33 Regularity of free boundaries in anisotropic capillarity problems and the validity of Young’s law, (with G. de Philippis), preprint 32 Rigidity of equality cases in Steiner’s perimeter inequality (with F. Cagnetti, M. Colombo, and G. De Philippis), preprint arXiv:1309.1639 31 Essential connectedness and the rigidity problem for Gaussian symmetrization (with F. Cagnetti, M. Colombo, and G. De Philippis), preprint arXiv:1304.4527. 30 Sharp stability inequalities for planar double bubbles (with M. Cicalese and G. P. Leonardi), preprint arXiv:1211.3698 29 Sharp stability inequalities for the Plateau problem (with G. De Philippis), accepted on Journal of Differential Geometry. 28 Quantitative stability in the isodiametric inequality via the isoperimetric inequality (with M. Ponsiglione and A. Pratelli), Trans. AMS. 366 (2014) 1141- 1160. 27 Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation (with A. Figalli and A. Pratelli), Adv. Math. 242 (2013), 80-101. 26 On the isoperimetric problem with respect to a log-convex density (with A. Figalli), Calc. Var. PDE 48 (2013), 447-489. 25 A geometric approach to correlation inequalities in the plane (with A. Figalli and A. Pratelli), Ann. Inst. H. Poincaré Prob. 50 (2014), 1-14. 24 On the isoperimetric problem with respect to a mixed Euclidean-Gaussian density (with N. Fusco and A. Pratelli), J. Funct. Anal. Volume 260, 12 (2011), 3678-3717. 23 On the shape of liquid drops and crystals in the small mass regime (with A. Figalli), Arch. Ration. Mech. Anal. Volume 201, Number 1, 143-207 . 22 On the isoperimetric deficit in the Gauss space (with A. Cianchi, N. Fusco and A. Pratelli), American J. Math.133 (2011), 131-186. 21 Exact reconstruction of color images by a total variation model (with I. Fonseca, G. Leoni and M. Morini), Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), 1291-1331. 20 A mass transportation approach to quantitative isoperimetric inequalities (with A. Figalli and A. Pratelli), Invent. Math, 182, (2010), 167-211. 19 A note on Cheeger sets (with A. Figalli and A. Pratelli), Proc. AMS 137 (2009), no. 6, 2057–2062. 18 A refined Brunn-Minkowski inequality for convex sets (with A. Figalli and A. Pratelli), Ann. Inst. H. Poincaré Anal. Non Linéaire, 26 (2009), 2511-2519. 17 The sharp Sobolev inequality in quantitative form (with A. Cianchi, N. Fusco and A. Pratelli), J. Eur. Math. Soc. (JEMS) 11 (2009), no. 5, 1105–1139. 16 Stability estimates for certain Faber-Krahn, isocapacitary and Cheeger inequalities (with N. Fusco and A. Pratelli), Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 8 (2009), no. 1, 51–71. 15 Some methods for studying stability in isoperimetric type problems, Bull. AMS 45 (2008), 367-408. 14 The sharp quantitative isoperimetric inequality (with N. Fusco and A. Pratelli), Ann. of Math. (2008), no. 3, 941-980. 13 Balls have the worst best Sobolev inequalities. Part two: variants and extensions (with C. Villani), Calc. Var. PDE, 31 (2008), no. 1, 47-74. 12 Confining thin elastic sheets and folding paper (with S. Conti), Arch. Ration. Mech. Anal. 187 (2008), no. 1, 1-48. 11 The sharp quantitative Sobolev inequality for functions of bounded variation (with N. Fusco and A. Pratelli), J. Funct. Anal. 244 (2007), n.1, pp.315-341. 10 Rigorous derivation of Föppl’s theory for clamped elastic membranes leads to relaxation (with S. Conti and S. Müller), SIAM J. Math. Anal. 38 (2006), no. 2, 657-680. 9 A remark on Serrin’s theorem (with N. Fusco and M. Gori), NoDEA, 13 (2006), no.4, 425-433. 8 Rank-one convex functions on 2 × 2 symmetric matrices and laminates on rank- three lines (with S. Conti, D. Faraco and S. Müller), Calc. Var. PDE (2005), no. 4, 479-493 7 Balls have the worst best Sobolev inequalities (with C. Villani), J. Geom. Anal. 15 (2005), no. 1, 83–121. 6 A new approach to counterexamples to L1 estimates: Korn’s inequality, geometric rigidity and regularity for gradients of separately convex functions (with S. Conti and D. Faraco), Arch. Ration. Mech. Anal. 175 (2005), no. 2, 287– 300. 5 The common root of the geometric conditions in Serrin’s lower semicontinuity theorem (with M. Gori), Ann. Mat. Pura e Applicata, 184 (2005), no. 1, 95–114. 4 A Γ-convergence result for variational integrators of quadratic lagrangians (with M. Morini), ESAIM: COCV 10 (2004), n. 4, 656-665. 3 On the relaxation on BV of certain non coercive integral functionals, J. Convex Anal. 10 (2003), n. 2, 477-489. 2 On the lower semicontinuity of supremal functionals (with M. Gori), ESAIM: COCV 9 (2003), 135-143. 1 On some sharp conditions for lower semicontinuity in L1 (with M. Gori and P. Marcellini), Diff. Int. Equations 16 (2003), no.1, 51-76.
Books and lecture notes: 2 Sets of finite perimeter and geometric variational problems: an introduction to Geometric Measure Theory, Cambridge Studies in Advances Mathematics 135, Cambridge University Press, 2012. 1 Symmetrization, optimal transport and quantitative isoperimetric inequalities. This is a chapter in: Optimal transportation, Geometry and Functional inequalities. Proceedings of the school held in Pisa, October 2008. Edited by Luigi Ambrosio. Centro di Ricerca Matematica Ennio De Giorgi (CRM) Series, 11. Edizioni della Normale, Pisa, 2010.
Citations: Mathscinet indexes 27 of the above papers, with 242 citations by 173 authors.
Research grants: 4 Stability, symmetry and regularity issues in geometric variational problems, NSF Grant DMS-1265910, from 7/13 to 6/16 (as principal investigator) 3 Analysis of optimal sets and optimal constants: old questions and new results, ERC Starting Grant 258685, from 8/10 to 7/16 (as co-investigator, principal investigator Aldo Pratelli); I am currently not participating to this project 2 Analytic techniques for geometric and functional inequalities, ERC Advanced Grant 246923, from 1/09 to 12/15 (as co-investigator, principal investigator Nicola Fusco); I am currently not participating to this project. 1 Geometric-functional inequalities in sharp and quantitative form, GNAMPA- INdAM, from 1/07 to 12/07.
Research grants (pending): 1 FRG: Collaborative Research: Vectorial and geometric problems in the Calculus of Variations, other PIs A. Figalli (UT Austin), L. C. Evans (Berkley), O. Savin (Columbia U.)
Referee activity (journals): SIAM J Math Anal, Arch. Rat. Mech. Anal., Inv. Math., ESAIM COCV, NoDEA, Proc. Royal Soc. Edinburgh, Geom. Funct. Anal, J. Funct. Anal, Annali SNS Pisa, J Potential Theory, J Diff Equations, Duke Math J, Ann. of Math.
Referee activity (grants): 1 Blanc SIMI 1 2011 Programme, Agence Nationale de la Recherche. 2 VQR 2004-2010 (research evaluation of the Italian university system for the period 2004- 2010).
Editorial work: I have been invited to edit a special issue on Geometric Measure Theory by the Bollettino dell’Unione Matematica Italiana.
Graduate students advising: I am currently advising two graduate students at UT Austin: Robin Neumayer (joint with A. Figalli) and Cornelia Mihaila.
Undergraduate students advising: - Marco Caroccia, Stime asintotiche per partizioni minimali del piano, Master Degree in Mathematics, U Firenze, 7/11 - Berardo Ruffini, Riduzione al caso radiale per una versione quantitative della disuguaglianza di Gagliardo-Nirenberg, Master Degree in Mathematics, 4/10.
Invited graduate courses and courses in research schools: 5 The rigidity problem for symmetrization inequalities, ERC school "Geometric functional inequalities and shape optimization", Napoli, Accademia Pontaniana, September 2013. 4 Geometric variational problems, University of Florence, June 2013. 3 Equilibrium shapes for anisotropic surface tension energies, Crash Courses in Analysis and Nonlinear PDEs, organized by the Centre for Analysis and Nonlinear PDEs at Heriot-Watt University of Edinburgh in collaboration with the Oxford Centre for Nonlinear PDE at Oxford University, February 2010. 2 Symmetrization, optimal transport and quantitative isoperimetric inequalities, during the school Optimal transportation, geometry and functional inequalities, organized by the Scuola Normale Superiore di Pisa. The lecture notes of this course have been published by the SNS Pisa, October 2008. 1 Geometric-functional inequalities in sharp and quantitative form, PhD course, University of Napoli “Federico II”. The lecture notes of this course have been published on the Bulletin of the American Mathematical Society ([15] in the list of publications), May 2007.
Workshops and school organization: 1 Calculus of Variations, Continuum Mechanics and Geometric Inequalities (6/11) organized with Aldo Pratelli.
Invited talks: 53 Geometric properties of perturbed bubbles and double-bubbles, Colloquium talk, Mitchigan State University, 11/13 52 The rigidity problem for symmetrization inequalities, joint Basel-Freiburg- Zurich seminar, University of Zurich, 10/13. 51 The rigidity problem for symmetrization inequalities, Rutgers University, New Brunswick, 10/13. 50 Rigidity of equality cases in symmetrization inequalities, Workshop on PDEs, MFO, Oberwolfach, 8/13. 49 Geometric properties of perimeter minimizing soap-bubble clusters, Workshop on “Geometric Measure Theory and Optimal Transport”, ICTP Trieste, 7/13 48 Essential connectedness and rigidity problems in symmetrization inequalities, UCLA, Los Angeles, 5/13. 47 Essential connectedness and rigidity problems in symmetrization inequalities, University of Sussex, Brighton, 5/13. 46 Global stability inequalities for the Plateau problem, Workshop Geometric inequalities in the Calculus of Variations, Pisa, 7/12. 45 Sharp stability estimates for the Plateau problem, University of Houston, Texas, USA, 3/12. 44 Sharp stability estimates in geometric variational problems, Erlangen- Nurnberg University, Germany, 1/12. 43 Sharp stability estimates for the Plateau problem, Math Colloquium, Carnegie Mellon University, 12/11. 42 Sharp stability estimates for the Plateau problem, Analysis Applied Math Seminar, U Toronto, 11/11 41 Sharp stability estimates in geometric variational problems, Dep Math U Texas at Austin, 10/11 40 The isoperimetric problem with respect to a symmetric density, Dip Mat U Roma Tor Vergata, 2/11 39 Sulla caratterizzazione dei minimi nei problemi isoperimetrici rispetto a densità simmetriche, Workshop ”XXI Convegno Nazionale di Calcolo delle Variazioni”, Levico Terme, 2/11 38 The isoperimetric problem with respect to a symmetric density, Dip Mat U Padova, 1/11 37 The isoperimetric problem with respect to a symmetric density, Dip Mat U Roma la Sapienza, 1/11 36 An isoperimetric inequality of mixed Euclidean-Gaussian type, Intensive trimester on Calculus of Variations, Singular Integrals and Incompressible Flows, ICMAT, Madrid, 9/10. 35 An overview on sharp stability inequalities in isoperimetric problems, GNAMPA- ERC Summer school, 6/10. 34 Stability problems for anisotropic surface tensions, Dip Fis U Roma Tor Vergata, 11/09. 33 Stability problems for anisotropic surface tensions, Dip Mat U Ferrara, 11/09 32 Stability problems for anisotropic surface tensions, Workshop Recent advances in optimal transportation and applications, Nice, 10/09. 31 Stability problems for anisotropic surface tensions, Workshop Optimal transportation: theory and applications, Institut Fourier, Grenoble, 6/09. 30 Stability problems for anisotropic surface tensions, Mini-symposium in PDEs, Maxwell Institute Centre for Analysis and Nonlinear PDEs Edinburgh, 5/09. 29 Stability problems for crystals, Workshop Advances in Mathematical Analysis, EPFL Lausanne, 3/09. 28 Sulla forma dei cristalli di massa piccola, Dip Mat U Napoli ”Federico II”, 1/09 27 Symmetrization, optimal transport and quantitative isoperimetric inequalities. Workshop Glimpses of Geometry, ENS-Lyon, 5/08. 26 Trasporto di massa e stabilità nel problema di Wulff. Workshop XVIII Convegno Nazionale di Calcolo delle Variazioni, Levico Terme, 2/08. 25 Stability properties of the Wulff shape via mass transportation, Séminaire d’Analyse Fonctionnelle, UMPC (Paris 6), 12/07. 24 Una stima di stabilità per il problema isoperimetrico relativo a un perimetro anisotropo, Dip Mat U Pisa, 12/07. 23 Stability properties of the Wulff shape via mass transportation, CNA CMU Pittsburgh, 11/07. 22 L’energia elastica necessaria a comprimere un foglio di carta. Workshop XVIII Congresso dell’Unione Matematica Italiana, 10/07. 21 Stability properties of the Euclidean isoperimetric inequality, U Duisburg- Essen, 6/07 20 A stability estimate for the first eigenvalue of the p-Laplacean. Workshop New trends in PDEs and Calculus of Variations, Cortona, 5/07. 19 Una forma quantitativa della disuguaglianza di Sobolev, U Roma Tor Vergata, 3/07. 18 Una forma quantitativa della disuguaglianza di Sobolev. Workshop Calcolo delle Variazioni e Teoria Geometrica della Misura, Levico Terme, 2/07. 17 Una versione quantitativa della disuguaglianza di Sobolev, Dip Mat U Firenze, 1/07. 16 The sharp quantitative Sobolev inequality for functions of bounded variation, CNA CMU Pittsburgh, 11/06. 15 The quantitative Sobolev inequality in the supercritical case. Summer School on Calculus of Variations and Applications, Ponta Delgada, Azores, 9/06. 14 The isoperimetric inequality in a sharp, quantitative form. Workshop Optimal Transport and Geometric PDE’s, Nice, 6/06. 13 Confining thin elastic sheets and folding paper, SISSA, Trieste, 3/06. 12 The sharp quantitative isoperimetric inequality, Institut für Mathematik, U Zürich, 2/06. 11 Confining thin elastic sheets and folding paper. Workshop Multiscale Problems in Quantuum Mechanics and Averaging Techniques, Weierstrass Institute, Berlin, 9/05. 10 L’energia elastica necessaria a comprimere un foglio di carta e questioni matematiche collegate, Dip Mat U Napoli ”Federico II”, 4/05. 9 Isometric embeddings and scaling laws for compressed elastic sheets. Workshop Recent Advances in Calculus of Variations and PDE’s: a young researchers meeting, Dip. Matematica Tonelli, Pisa, 3/05. 8 Isometric embeddings and scaling laws for compressed elastic sheets, Arbeitsgmeinschat Mikrostrukturen, MPI-MIS, Leipzig, 1/05. 7 Sul problema della regolarità delle funzioni rango-uno convesse. Workshop Calcolo delle Variazioni e Teoria Geoemetrica della Misura, Lizzanello, Centro Polifunzionale Ennio De Giorgi, 10/04. 6 A new approach to counterexamples to L1 estimates: Korn’s inequality and geometric rigidity. Workshop Dislocation Patterns in Plastic Materials, Warwick, 5/04. 5 Le sfere hanno la peggior disuguaglianza di Sobolev ottimale, Dip Mat U Firenze, 4/04. 4 Le palle hanno la peggior disuguaglianza di Sobolev ottimale. Workshop Calcolo delle Variazioni e Teoria Geometrica della Misura, Levico Terme, 2/04. 3 Transport of mass and sharp Sobolev inequalities with trace terms, Arbeitsgmeinschat Mikrostrukturen, MPI-MIS, Leipzig, 11/03.3 Le sfere hanno la peggior disuguaglianza di Sobolev ottimale, Dip Mat U Firenze, 2/04. 2 The common root of the geometric conditions in Serrin’s lower semicontinuity theorem, School on Mass Transportation (Ambrosio and Villani organizers) MFO, Oberwolfach, 10/02. 1 Hoelderianità e semicontinuità inferiore in L1 Workshop Calcolo delle Variazioni e Teoria Geometrica della Misura, Levico Terme, 2/02
Visited institutions: - Institute for Computational Engineering and Sciences, Austin Texas, from 8/11 to 5/12 - Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany, from 10/02 to 12/02 and from 10/03 to 12/03 - Center for Nonlinear Analysis, Carnegie Mellon University, Pittsburgh, US, from 1/03 to 5/03, on 11/06, and on 11/07 - Institut für Angewandte Mathematik Abteilung für Mathematische Methoden der Physik, Bonn, Germany, on 7/04 - Hausdorff Research Institute for Mathematics, Bonn, Germany, Junior Trimester Program on Analysis Group “Calculus of Variations and Image Processing”, 9/08. - Institut für Angewandte Mathematik, Bonn, from 9/10
Teaching: - M372K Partial differential equations and applications, UT Austin, Spring 14 - M361 Functions of one complex variable, UT Austin, Fall 13 - M361K Introduction to Real Analysis, UT Austin, Spring 13 - M361 Functions of one complex variable, UT Austin, Fall 12 - Calculus of Variations (Spring 08, 09, 10, Fall 10), U Firenze. The course presents the Direct Methods in the Calculus of Variations for scalar valued problems. Topics included are: sets of finite perimeter and Sobolev functions, Lipschitz minimizers and barriers, regularity for solutions of elliptic equations in divergence form and of minimizers of uniformly convex problems (http://web.math.unifi.it/users/maggi/calcvar.html) - Introduction to sets of finite perimeter and functions of bounded variation (Spring 2005) U Duisburg-Essen. The lecture notes from this course are the original nucleus of the book with Cambridge University Press. - Calculus for students in Biology (Fall 05, 06, 07, 08, 09, 10) and Chemistry ( Fall 05, 06, 07), U Firenze; - Exercise sessions on Functional Analysis (Spring 05), U Duisburg-Essen.
Service: - Postdoc hiring committee, Department of Mathematics, UT Austin (2012 and 2013). - Collegio dei docenti (Graduate school committee), Dipartimento di Matematica U. Dini, U. Firenze, (2010 and 2011).