CURRICULUM VITAE GIAN PAOLO LEONARDI

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1 CURRICULUM VITAE GIAN PAOLO LEONARDI PERSONAL INFORMATION Family name, First name: Leonardi, Gian Paolo Date and place of birth: November 18 th, 1970; Modena (Italy) Family status: married, with two children ECAS ID: nlegianp Web page: EDUCATION 01/01/ /12/1998. PhD in Mathematics, Dipartimento di Matematica, Università di Trento (Italy). 01/10/ /06/1994. Degree in Mathematics, University of Modena (Italy). CURRENT POSITION 01/11/2005 today. Assistant Professor, Dipartimento di Scienze Fisiche, Informatiche e Matematiche (FIM), Università di Modena e Reggio Emilia (Italy). PREVIOUS POSITION 01/11/ /11/2005. Assistant Professor, Dipartimento di Metodi e Modelli Matematici, Università di Padova (Italy). CURRENT RESEARCH INTERESTS Variational problems and Geometric Measure Theory in Euclidean and sub-riemannian geometry. The present interests include: (1) isoperimetric-type problems for sets and clusters, with special focus on quantitative stability and on the Cheeger problem; (2) discrete varifolds: theory and applications to geometric variational problems and image analysis; (3) Geometric measure theory in sub-riemannian spaces. FELLOWSHIPS AND RESEARCH CONTRACTS 01/05/ /07/2004. CNRS Research Contract, Lab. J.L.Lions, University of Paris VI (France). 06/05/ /06/2003. TMR Research Contract, Lab. J.L.Lions, University of Paris VI (France). 01/06/ /09/2002. CNRS Research Contract, Lab. J.L.Lions, University of Paris VI (France). 01/10/ /03/2002. CNR Fellowship, Dep. de Mathematiques, University of Paris XI - Orsay (France). 1

2 2 GIAN PAOLO LEONARDI 01/07/ /06/2001. Post-doctoral fellowship, Dipartimento di Matematica, Università di Trento (Italy). VISITING SCHOLARSHIPS Department of Mathematics - Univ. Texas at Austin (March-April 2016). Department of Mathematics - Univ. Texas at Austin (April two weeks). Departamento de Geometría y Topología - Univ. Granada (May one month). Department Mathematik - Universität Erlangen (February one week). Zentrum Mathematik - Technische Universität München (February one week). Max Planck Institute Mathematik - Leipzig (May-June one week). Laboratoire J.-A.Dieudonné - Univ. Nice Sophia Antipolis (April one week). Department Mathematik - Freie Universität Berlin (June-July two months). Department of Mathematics - University of Helsinki (May two weeks). PROJECTS Spanish project MTM C2-1-P, entitled: Desigualdades geométricas. 01/01/ /12/2016 (foreign member). PRIN : Calcolo delle Variazioni. 01/02/ /02/2016 (member). PRIN 2008: Disuguaglianze e problemi variazionali in strutture metriche riemaniane e subriemaniane. 22/03/ /09/2012 (member). PRIN 2006: Teoria geometrica della misura e problemi variazionali in strutture metriche riemaniane e subriemaniane. 09/02/ /02/2009 (member). PRIN 2004: Calcolo delle Variazioni 1)Teoria geometrica della misura in spazi euclidei e in gruppi di Carnot. 2)Funzionali di Ginzburg-Landau. 3)G-convergenza. 30/11/ /11/2006 (member). PRIN 2002: Calcolo delle Variazioni: 1) teoria geometrica della misura in spazi euclidei ed in gruppi di Carnot; 2) funzionali di Ginzburg-Landau. 16/12/ /12/2004 (member). GNAMPA 2016: Variational problems and Geometric Measure Theory in metric spaces. 21/03/2016 (coordinator). GNAMPA 2015: Problemi isoperimetrici e Teoria Geometrica della Misura in spazi metrici. 12/03/2015 (member). GNAMPA 2014: Problemi di regolarità e di Teoria Geometrica della Misura in spazi metrici. 11/03/2014 (member). GNAMPA 2012: Problemi di evoluzione e Teoria Geometrica della Misura in spazi metrici. 09/05/2012 (member). GNAMPA 2011: Problemi geometrici, variazionali ed evolutivi in strutture metriche. 27/04/2011 (member). GNAMPA 2010: Problemi geometrici, variazionali ed evolutivi in strutture metriche. 30/03/2010 (coordinator). GNAMPA 2009: Metodi geometrici per analisi in spazi non Euclidei; spazi metrici doubling,

3 CURRICULUM VITAE 3 gruppi di Carnot e spazi di Wiener. 01/03/2009 (member). GNAMPA 2008: Mappe, misure e calcolo nonlineare nei gruppi stratificati. 30/03/2008 (member). SUPERVISION OF GRADUATE AND PHD STUDENTS Supervision of 10 Degree theses and 5 Master theses in Mathematics. Currently supervising Giorgio Saracco s PhD thesis (within the consortium between the Universities of Ferrara, Modena-Reggio Emilia, and Parma). Supervision of the PhD thesis of Blanche Buet (co-advised with Simon Masnou at the University of Lyon 1 - France; thesis defended on December 2014). 30/06/ /07/2014. Member of the jury for PhD defense of Efstratios Vernadakis, University of Granada (Spain). 18/06/ /06/2012. Member of the jury for PhD defense of Matteo Galli, University of Granada (Spain). TEACHING ACTIVITIES Courses for the Degree / Master in Mathematics: 01/11/2005 today. Courses: Calculus 1, Calculus 2, Functional Analysis, Partial Differential Equations, Measure Theory and Integration, given at the University of Modena and Reggio Emilia (Italy). 01/11/ /11/2005. Courses: Calculus 1, Calculus 2 at the University of Padova (Italy). 01/10/ /11/2001. Courses: Calculus 1, Calculus 2 at the University of Trento (Italy). PhD Courses: Regularity theory for Lambda-minimizers of the perimeter, PhD in Mathematics - University of Modena and Reggio Emilia. 09/05/ /06/2013. Regularity theory for Lambda-minimizers of the perimeter at the Department of Geometry and Topology - University of Granada (Spain). 18/06/ /06/2012. Quantitative isoperimetric inequalities, Departamento de Geometría y Topología - University of Granada (Spain). 21/05/ /05/2012. Quantitative isoperimetric inequalities, Max Planck Institute - Leipzig (Germany). 17/03/ /03/2011. Quantitative isoperimetric inequalities, Rencontres d Analyse 2011, Institute Camille Jordan - University of Lyon 1 (France). ORGANIZATION OF SCIENTIFIC MEETINGS AND COURSES 15/02/ /02/2007. Focus Meeting on Geometric Measure Theory and Least-Area Problems, University of Modena and Reggio Emilia (with lectures by G. David, N. Fusco, F. Morgan, M. Ritoré). Minicourses in Analysis, University of Padua (editions 2003, 2004, 2005).

4 4 GIAN PAOLO LEONARDI DISSEMINATION Since 2005, I propose a Soap Bubble Laboratory for high school students at my department, sponsored by the italian project Progetto Lauree Scientifiche. February Public conference on soap bubbles and soap films at the University of Modena and Reggio Emilia (joint with Prof. Frank Morgan, Williams College - USA). September Soap bubble Lab for the European Researcher s Night in Trento. September Soap Bubble Lab for the European Researchers Night in Modena. INVITED PRESENTATIONS (selection 2010 today) ( February) XXVII Convegno di Calcolo delle Variazioni e Teoria Geometrica della Misura (Levico, TN). Title of the talk: Weak normal traces, super-reduced boundary, and an application to the PMC equation ( April) Talk at the Department of Mathematics - Carnegie Mellon Univ. Pittsburgh (Pennsylvania, US). Title: Discrete varifolds: theory and applications ( April) Talk at the Department of Mathematics - UT Austin (Texas, US). Title: Discrete varifolds: theory and applications ( July) Talk at the summer school Geometric Measure Theory and Calculus of Variations: Theory and Applications held in Grenoble (France). Title: Towards a unified theory of surface discretization. ( April) Talk at the Department of Mathematics - UT Austin (Texas, US). Title: Cheeger sets and capillarity. ( January) Talk at the Institüt für Analysis - TU Dresden (Germany). Title: Cheeger sets in strips and nonconvex domains. ( December) Talk at the Department für Mathematik, University of Köln (Germany). Title: Cheeger sets in strips and nonconvex domains. ( June) Talk at the Nuclear Physics Institute, Czech Academy of Sciences - Prague (Czech Republic). Title: The Cheeger problem for non-convex domains. ( May) Talk at the Math Department of the University of Jÿvaskÿla (Finland). Title: The Cheeger problem: an overview. ( April) Talk at the Math Department of the University of Ferrara. Title: Properties of Cheeger sets in non-convex domains. ( January) Giornate di lavoro su Calcolo delle Variazioni e Teoria Geometrica della Misura (Levico Terme - Italy). Title of the talk: Properties of Cheeger sets in non-convex domains. ( September) Invited speaker at the workshop New trends in shape optimization (Erlangen - Germany). Title of the talk: The Cheeger problem in planar domains. ( May) Talk at the Department of Geometry and Topology, Univ. Granada, entitled Stability inequalities for perimeter-minimizing clusters ( February) Giornate di lavoro su Calcolo delle Variazioni e Teoria Geometrica della

5 CURRICULUM VITAE 5 Misura (Levico Terme). Title of the talk: Stability inequalities for perimeter-minimizing clusters. ( July) Invited speaker at the workshop Geometric Inequalities in Calculus of Variations (De Giorgi Center, Pisa - Italy). Title of the talk: Quantitative stability for perimeter-minimising clusters. ( June) Invited speaker at the Summer School Calculus of variations, continuum mechanics and geometric inequalities. Title of the talk: A new approach to quantitative isoperimetric inequalities. ( November) Talk at the Math Department, University of Firenze: A Selection Principle for quantitative isoperimetry. ( June) Talk at the University of Trento: A variational approach to quantitative isoperimetry. ( March) Invited speaker at the conference New trends in Sub-Riemannian Geometry (Nice - France). Title of the talk: A regularity result for strictly abnormal minimisers. ( February) Giornate di lavoro su Calcolo delle Variazioni e Teoria Geometrica della Misura (Levico Terme - Italy). Title of the talk: Su una congettura di Hall per la disuguaglianza isoperimetrica quantitativa. MAIN PUBLICATIONS AND PREPRINTS CICALESE M., LEONARDI G.P., MAGGI F., Sharp stability inequalities for planar double bubbles, accepted on Interfaces and Free Boundaries (2017). BUET B., LEONARDI G.P., MASNOU S., A varifold approach to surface approximation. Submitted (2016) LEONARDI G.P., SARACCO G., On the prescribed mean curvature equation in weakly regular domains. Submitted (2016) LEONARDI G.P., RITORÉ M., VERNADAKIS E., Isoperimetric inequalities in unbounded convex bodies. Submitted (2016) LE DONNE E., LEONARDI G.P., MONTI R., VITTONE D., Extremal polynomials in stratified groups, accepted on Comm. Anal. and Geom. (2016). LEONARDI G.P., MAGGI F., Improved convergence theorems for bubble clusters. II. The three-dimensional case. Accepted on Indiana Univ. Math. J. (2016) CICALESE M., LEONARDI G.P., MAGGI F., Improved convergence theorems for bubble clusters. I. The planar case. Accepted on Indiana Univ. Math. J. (2016) BUET B., LEONARDI G.P., Recovering measures from approximate values on balls. Ann. Acad. Sci. Fenn., 41, pp (2016) LEONARDI G.P., PRATELLI A., On the Cheeger sets in strips and non-convex domains, Calc. Var. PDE, 55 (1), pp (2016). BUET B., LEONARDI G.P., MASNOU S., Discrete varifolds: a unified framework for discrete approximations of surfaces and mean curvature, Proceedings SSVM 2015, LNCS volume 9087

6 6 GIAN PAOLO LEONARDI (2015). FRANCESCHI V., LEONARDI G.P., MONTI R., Quantitative isoperimetric inequalities in H n, Calc. Var. Partial Differential Equations, 54, pp (2015). BUET B., LEONARDI G.P., MASNOU S., Discrete varifolds and surface approximation, Shape and Topological Optimization, 2014, RICAM. LEONARDI G.P., An overview on the Cheeger problem, New trends in shape optimization - International Series of Numerical Mathematics, Birkhäuser, ISBN-13: (2015). LE DONNE E., LEONARDI G.P., MONTI R., VITTONE D., Corners in non-equiregular sub-riemannian manifolds, ESAIM COCV, vol. 21 (3), pp (2015). LE DONNE E., LEONARDI G.P., MONTI R., VITTONE D., Extremal curves in nilpotent Lie groups, Geom. Funct. Anal. (GAFA), Vol. 23 (4), pp (2013). CICALESE M., LEONARDI G.P., Best constants for the isoperimetric inequality in quantitative form, J. Eur. Math. Soc. (JEMS), Vol.15 (3), pp (2013). CICALESE M., LEONARDI G.P., A Selection Principle for the sharp quantitative isoperimetric inequality, Arch. Rational Mech. Anal. 206, pp (2012). LEONARDI G.P., RIGOT S., VITTONE D., Isodiametric sets in the Heisenberg group, Rev. Mat. Iberoam. 28 (2012), no. 4, LEONARDI G.P., Un nuovo approccio alle disuguaglianze isoperimetriche quantitative. Bruno Pini Mathematical Analysis Seminar, [S.l.]. ISSN (2011). LEONARDI G.P., MAGNANI V., Intersections of intrinsic submanifolds in the Heisenberg group, J. Math. Anal. Appl., 378(1): (2011). LEONARDI G.P., MASNOU S., Locality of the mean curvature of rectifiable varifolds, Adv. Calc. Var., Vol 2 (1), pp (2009). LEONARDI G.P., MONTI R., End-point equations and regularity of abnormal sub-riemannian geodesics, Geom. Funct. Anal. (GAFA), Vol. 18 (2), pp (2008). LEONARDI G.P., TILLI P., On a constrained variational problem in the vector valued case, J. Math. Pures Appl., Vol. 85 (2), pp (2006). LEONARDI G.P., MASNOU S., On the isoperimetric problem in the Heisenberg group H n, Ann. Mat. Pura Appl. (4) 184, n.4, pp (2005). LEONARDI G.P., RIGOT S., Isoperimetric sets on Carnot groups. Houston J. Math. vol. 29 (3), pp (2003). LEONARDI G.P., Gamma-Convergence of constrained Dirichlet functionals. Boll. Unione Matematica Italiana, Vol. 6-B (8), pp (2003). LEONARDI G.P., TAMANINI I., Metric spaces of partitions and Caccioppoli partitions. Adv. Math. Sci. Appl., Vol. 12 (2), pp (2002). LEONARDI G.P., Partitions with prescribed mean curvatures. Manuscripta Math., Vol. 107, pp (2002). LEONARDI G.P., Infiltrations in immiscible fluids systems, Proc. Roy. Soc. Edinburgh, 131A, pp (2001). LEONARDI G.P., Blow-up of oriented boundaries, Rend. Sem. Mat. Univ. Padova, 103, pp.

7 CURRICULUM VITAE (2000). LEONARDI G.P. - TAMANINI I., On minimizing partitions with infinitely many components, Ann. Univ. Ferrara - Sez. VII - Sc. Mat., Vol. XLIV, pp (1998). LEONARDI G.P., Optimal subdivisions of n-dimensional domains, Ph.D. thesis (Trento, 1998). OTHER PUBLICATIONS LEONARDI G.P., Il mistero isoperimetrico di Zenodoro (Zenodorus isoperimetric mystery), in Vedere la Matematica... alla maniera di Mimmo Luminati, Edizioni ETS, Pisa (2015). MERANI M.L., LEONARDI G.P., SALADINO D., A Model to Seize the Instantaneous Performance of P2P Streaming Platforms: Simulative and Experimental Validation, Global Telecommunications Conference, GLOBECOM IEEE. MERANI M.L., LEONARDI G.P., SALADINO D., Taking Advantage of Social Network Relationships in P2P Streaming Overlays, Global Telecommunications Conference, GLOBE- COM IEEE. MERANI M.L., LEONARDI G.P., SALADINO D., Scalability and Peer Churning in IP-TV: an Analytical Insight, Global Telecommunications Conference, GLOBECOM IEEE. CIATTI P., GONZALEZ E.H., LANZA M., LEONARDI G.P. (editors), Topics in Mathematical Analysis, World Scientific Publisher (2008). LEONARDI G.P., PARONETTO F., PUTTI M., Effective anisotropy tensor for the numerical solution of flow problems in heterogeneous porous media, Proc. CMWR XVI International Conference, Copenhagen, Denmark, June (2006) AWARDS Séminaire Bourbaki (IHP - 19 marzo 2016). Speaker: Ludovic Rifford. Title: Singulières minimisantes en géométrie sous-riemanniennes [d après Hakavuori, Le Donne, Leonardi, Monti...]. (last update: March 2, 2017)