Curriculum Vitae Samuele Mongodi

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1 Curriculum Vitae Samuele Mongodi Personal Details Name: Samuele Mongodi Address (Office): p/o Università di Roma Tor Vergata, Dipartimento di Matematica, Via della Ricerca Scientifica, I Rome (Italy) Home-page: Education 15/03/ present PostDoc at the University of Rome Tor Vergata, for the programmes PRIN Varietà reali e complesse: geometria, topologia e analisi armonica (Real and complex varieties: geometry topology and harmonic analysis) and ERC Holomorphic Evolution Equations (under the supervision of prof. Filippo Bracci) PostDoc at the Scuola Normale Superiore in Pisa, for the programme FIRB - Analysis and Beyond (under the supervision of Dr. Carlo Mantegazza) Jul 2012 Earned a Ph.D. degree, grade 70/70 cum laude, defending a thesis titled Applications of metric currents to complex analysis. Advisor: prof. G. Tomassini PhD student at the Scuola Normale Superiore in Pisa (Corso di Perfezionamento). Advisor: prof. G. Tomassini. Oct 2008 First successful candidate (out of six) in the PhD admission exams for a PhD position in Mathematics at the Scuola Normale Superiore. Jul 2008 Received the Diploma di Licenza from the Scuola Normale Superiore, grade 60/60 cum Laude Post graduate student in Mathemtics at the University of Pisa. Earned a Master s Degree in Mathematics in June 2008, grade 110/110 cum Laude, defending the thesis Forme differenziali e correnti metriche su spazi complessi (Differential forms and metric currents on complex spaces). Advisor: prof. G. Tomassini Undergraduate student in Mathematics at the University of Pisa. Earned a Bachelor s Degree in Mathematics in July 2006, grade 110/110 cum Laude, with the dissertation Tecniche di uniformizzazione per superfici di Riemann (Uniformization techniques for Riemann surfaces). Supervisor: prof. F. Lazzeri. Sep 2003 Succesful candidate in the undergraduate admission exams for the Faculty of Sciences at the Scuola Normale Superiore. Jul 2003 Received a high school Diploma, grade 100/100, from Liceo Scientifico Vittorio Sereni, Luino (VA), Italy.

2 Language Skills My native language is Italian, I have a good knowledge of English (both written and spoken) and a basic knowledge of German. I attended courses on both languages while I was a student in Scuola Normale Superiore; in terms of european levels, level B2 in German and C1 in English. Teaching experiences 2008/09 - Geometria (esercitazioni) (exercises course of 24hrs for Biomedics Engineering students on Linear Algebra and Geometry) with prof. M. Forti 2009/10 - Algebra Lineare (esercitazioni) (exercises course of 24hrs for Biomedics Engineering students on Linear Algebra) with prof. M. Forti 2009/10 - Geometria Differenziale Complessa (esercitazioni) (exercises course of approx. 50 hrs for SNS Mathematics students on Complex Differential Geometry) with prof. G. Tomassini 2010/11 - Geometria ed Algebra Lineare (esercitazioni) (exercises course of approx. 24hrs for Construction Engineering students on Linear Algebra and Geometry) with prof. M. Forti 2010/11 - Geometria Iperbolica Complessa (esercitazioni) (exercises course of 18 hrs for SNS Mathematics students on Complex Hyperbolic Geometry) with prof. G. Tomassini 2011/12 - Geometria ed Algebra Lineare (esercitazioni) (exercises course of 36 hrs for Architecture and Construction Engineering students on Linear Algebra and Geometry) with prof. M. Forti 2011/12 - Analisi Complessa in più Variabili (esercitazioni) (exercises course for SNS Mathematics students on Analysis in Several Complex Variables) with prof. G. Tomassini 2012/13 - Geometria ed Algebra Lineare (esercitazioni) (exercises course of 36 hrs for Architecture and Construction Engineering students on Linear Algebra and Geometry) with prof. M. Forti 2013/14 - Analisi Matematica 1 (120hrs course for Energetic Engeneering students on Calculus and Analysis in one real variable) 2014/15 - Analisi Matematica 1 (tutoraggio) (exercises course of approx. 30 hours for Engeneering students on Calculus and Analysis in one and several real variables) with prof. G. Bellettini. For the courses for Engineering students, I prepared handouts, test papers, written notes and lectures. For the SNS courses, I held the whole exercises course. Informations on these courses and some teaching materials (in italian only) can be found online at mongodi/dida.html. Conferences and Schools In the last years I have been a regular participant to the following conferences and schools which are held every one or two years.

3 Progressi Recenti in Geometria Reale e Complessa, Levico (TN Italy), October Complex Analysis and Geometry, Levico (TN, Italy), June KAWA - Complex Analysis With Applications - School and Workshop, Toulouse-Albi (France) in January , Marseille (France) in January March 2014, Barcelona (Spain) in February 2012 CR Geometry and PDEs, Levico (TN, Italy), June Other selected conferences I attended Colloque international d analyse complexe, Jul, Luminy (Marseille, France) ERC School on Analysis in Metric Spaces and Geometric Measure Theory, Jan 2011, Pisa (Italy) Geometric Methods of Complex Analysis, Apr Oberwolfach (Germany) A conference in honor of Pierre Dolbeault, 2-4 Jun Paris (France) Summer School and Workshop: Differential Forms on Singular Complex Spaces, 30 Jun - 4 Jul Bonn (Germany) Selected Talks and Seminars Levico, Jun min talk, titled Currents on singural complex spaces: the equation in the conference Complex Analysis and Geometry - XX Levico, Jun min talk titled equation in Banach spaces in the conference CR Geometry and PDEs - V - In honor of J.J. Kohn in his 80th Birthday Levico, Oct min talk, titled Correnti metriche positive e catene olomorfe negli spazi di Hilbert (Positive metric currents and holomorphic chains in Hilbert spaces) in the conference Progressi Recenti in Geometria Reale e Complessa Göteborg (SE), Sep min talk, titled Metric currents in complex geometry for the Complex Analysis Seminars (KASS) in Chalmers University Parma, Feb hr talk, titled Classification of weakly complete complex surfaces for the Geometry Seminar of the Department of Mathematics - University of Parma. Vienna (AT), Dec hr talk, titled Weakly complete complex surfaces for the Complex Analysis Seminars of the Faculty of Mathematics - Universität Wien. Research periods Chalmers University, Göteborg, Sweden, from 8/9/2013 to 15/9/2013, invited by prof. R. Berman.

4 Università di Parma - Dipartimento di Matematica, Parma, from 11/02/2014 to 13/02/2014, invited by prof. A. Saracco. Universität Wien - Fakultät für Mathematik, Vienna, Austria, from 30/11/2014 to 7/12/2014, invited by dr G. Dalla Sala. Publications (with E. Amar) On L r hypoellipticity of solutions with compact support of the Cauchy- Riemann equation, arxiv: v1 [math.cv], Annali di Matematica Pura ed Applicata, August 2014, Volume 193, Issue 4, pp , DOI: /s Some application of metric currents to complex analysis, arxiv: [math.cv], Manuscripta Mathematica July 2013, Volume 141, Issue 3-4, pp , DOI: /s (with A. Saracco) Non compact boundaries of complex analytic varieties in Hilbert spaces, arxiv: [math.cv], Complex Manifolds. Volume 1, Issue 1, ISSN (Online) , DOI: /coma , July 2014 Positive metric currents and holomorphic chains in Hilbert spaces, arxiv: v1 [math.cv], (to appear in Revista Matemática Iberoamericana) (with V. Magnani and J. Malý) A low rank property and nonexistence of higher dimensional horizontal Sobolev sets, arxiv: [math.ap] (to appear in The Journal of Geometric Analysis), DOI: /s (with G. Tomassini) Transversally pseudoconvex semiholomorphic foliations (to appear in Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.) (with G. Tomassini) 1-complete semiholomorphic foliations, arxiv: [math.cv] (to appear in Transactions of the American Mathematical Society) (with C. Mantegazza and M. Rimoldi) The Cotton tensor and the Ricci Flow, (submitted) (with G. Catino and L. Mazzieri) Rigidity of gradient Einstein shrinkers, arxiv: [math.dg] (submitted) Fields of Interest and Research Weakly complete complex spaces The problem of classifying and characterizing in terms of holomorphic functions (or more generally geometric and algebraic properties related to the sheaf of holomorphic functions) wealy complete complex spaces can be very well seen as a kind of Levi problem. At the present time, only very partial results appear in literature and I ve been

5 working, together with G. Tomassini and Z. Slodkowski, at the classification of weakly complete surfaces. Many problems lay ahead in this field; apart from the obvious and quite challenging question of extending such results to higher dimension or to the singular setting, several questions arise on the nature and behavior of pluriharmonic and plurisubharmonic functions in presence of some complex analytic object. Metric Currents in Complex Analysis I am interested in Complex Analysis and Geometry, particularly in non smooth settings; as a main tool for this research, I ve been studying the theory of metric currents and, more generally, analysis on metric spaces. I am studying infinite dimensional complex manifolds, focusing on the Cauchy-Riemann equation and on some problems in CR geometry (finite dimensional CR submanifolds in a infinite dimensional complex space). In particular, I have been working on extensions of the results of Harvey and Lawson, concerning the boundary problem for holomorphic chains. More generally, I also tackled the study of the structure and behavior of positive metric currents on complex Hilbert spaces, highlighting their links with finite-dimensional complex subspaces. I also studied the Cauchy-Riemann equation on singular spaces and on manifolds with L p estimates, one of the main directions of research being a development of a theory á la Andreotti-Grauert. Subriemannian Geometry I ve become recently interested in some topics of subriemannian geometry, namely the (non)existence of horizontal surfaces of Sobolev class in the Heisenberg group and other CC spaces, the area and coarea formula in stratified groups and their applications, with the further aim of a better understanding of the currents obtained by duality from the Rumin complex. Riemannian Geometry Since February 2012, I am part of the programme FIRB - Analysis and Beyond, with the aim of studying the properties and possibly obtaining classification theorems for self-similar solutions of geometrics flows (e.g. the Ricci flow). In particular, I have been studying the evolution of some tensorial quantities related to the Ricci flow, namely the Bach tensor, the Cotton tensor and the York tensor, and the rigidity properties of gradient Einstein solitons, introduced by Catino and Mazzieri in 2012, related to the gradient flow associated to the Einsten-Hilbert action. Mathematical Olympiads Since 2004, I have been working with a committee of the Italian Mathematica Union (and I am a member of it since 2009) for the preparation of Italian Mathematical Olympiads; I actively take part in the writing of the problems for the competitions, in checking the papers of the National competition and in selecting the members of the Italian team for the Balkan Mathematical Competitions (BMO), Romanian Masters in Mathematics (RMM) and International Mathematical Competitions (IMO).

6 Since 2005, I have been teaching several short courses in high schools all around Italy, on topics from elementary mathematics (euclidean geometry, arithmetics, combinatorics, basic algebra of polynomials), as preparations for the mathematical olympiads. These lectures sum roughly up to 300 hours of teaching in more or less 100 different high schools.