Curriculum Vitae
Samuele Mongodi
Personal Details
Name: Samuele Mongodi
Address (Office): p/o Universit`a di Roma “Tor Vergata”, Dipartimento di Mate-matica, Via della Ricerca Scientifica, I-00133 Rome (Italy)
E-mail: mongodi@mat.uniroma2.it, s.mongodi@sns.it, samuele.mongodi@gmail.com
Home-page: http://www.mat.uniroma2.it/~mongodi/, https://sites.google.com/site/samuelemongodi/
Education
15/03/2014 - present PostDoc at the University of Rome “Tor Vergata”, for the pro-grammesPRIN “Variet`a 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) 2012-2014PostDoc at the Scuola Normale Superiore in Pisa, for the programme ”FIRB
-Analysis and Beyond” (under the supervision of Dr. Carlo Mantegazza)
Jul 2012Earned a Ph.D. degree, grade 70/70 cum laude, defending a thesis titled Applica-tions of metric currents to complex analysis. Advisor: prof. G. Tomassini
2009-2011PhD 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 2008Received the Diploma di Licenza from the Scuola Normale Superiore, grade 60/60 cum Laude.
2006-2008Post 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.
2003-2006 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 2003Received a high school Diploma, grade 100/100, from ”Liceo Scientifico Vittorio Sereni”, Luino (VA), Italy.
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 Enginee-ring 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
Ar-chitecture and Construction Engineering students on Linear Algebra and Geometry) with prof. M. Forti
2011/12-Analisi Complessa in pi`u Variabili (esercitazioni)(exercises course for SNS Mathe-matics students on Analysis in Several Complex Variables) with prof. G. Tomassini 2012/13 - Geometria ed Algebra Lineare (esercitazioni) (exercises course of 36 hrs for
Ar-chitecture 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 En-geneering 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 athttp:/www.mat.uniroma2.it/ 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.
• Progressi Recenti in Geometria Reale e Complessa, Levico (TN Italy), October 2008-2010-2012-2014
• Complex Analysis and Geometry, Levico (TN, Italy), June 2009-2011-2013
• KAWA - Complex Analysis With Applications - School and Workshop, Toulouse-Albi (France) in January 2010-2013, Marseille (France) in January 2011 - March 2014, Barcelona (Spain) in February 2012
• CR Geometry and PDEs, Levico (TN, Italy), June 2010-2012 Other selected conferences I attended
• ”Colloque international d’analyse complexe”, 13 - 17 Jul, 2009 - Luminy (Marseille, France)
• ”ERC School on Analysis in Metric Spaces and Geometric Measure Theory”, 10 - 14 Jan 2011, Pisa (Italy)
• ”Geometric Methods of Complex Analysis”, 10 - 16 Apr 2011 - Oberwolfach (Germa-ny)
• ”A conference in honor of Pierre Dolbeault”, 2-4 Jun 2014 - Paris (France)
• ”Summer School and Workshop: Differential Forms on Singular Complex Spaces”, 30 Jun - 4 Jul 2014 - Bonn (Germany)
Selected Talks and Seminars
Levico, Jun 2011- 30 min talk, titledCurrents on singural complex spaces: the∂ equation
in the conference ”Complex Analysis and Geometry - XX”
Levico, Jun 2012- 15 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 2012- 30 min talk, titledCorrenti 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”
G¨oteborg (SE), Sep 2013- 45min talk, titledMetric currents in complex geometryfor the Complex Analysis Seminars (KASS) in Chalmers University
Parma, Feb 2014 - 1hr talk, titled Classification of weakly complete complex surfaces for the Geometry Seminar of the Department of Mathematics - University of Parma. Vienna (AT), Dec 2014- 1hr talk, titledWeakly complete complex surfacesfor the Complex
Analysis Seminars of the Faculty of Mathematics - Universit¨at Wien.
Research periods
• Chalmers University, G¨oteborg, Sweden, from 8/9/2013 to 15/9/2013, invited by prof. R. Berman.
• Universit`a di Parma - Dipartimento di Matematica, Parma, from 11/02/2014 to 13/02/2014, invited by prof. A. Saracco.
• Universit¨at Wien - Fakult¨at f¨ur Mathematik, Vienna, Austria, from 30/11/2014 to 7/12/2014, invited by dr G. Dalla Sala.
Publications
• (with E. Amar)OnLrhypoellipticity of solutions with compact support of the
Cauchy-Riemann equation, arXiv:1111.3458v1 [math.CV], Annali di Matematica Pura ed Ap-plicata, August 2014, Volume 193, Issue 4, pp 999-1018, DOI: 10.1007/s10231-012-0312-8
• Some application of metric currents to complex analysis, arXiv:1112.1462 [math.CV],
Manuscripta Mathematica July 2013, Volume 141, Issue 3-4, pp 363-390, DOI: 10.1007/s00229-012-0575-9
• (with A. Saracco) Non compact boundaries of complex analytic varieties in Hilbert spaces, arXiv:1211.4646 [math.CV], Complex Manifolds. Volume 1, Issue 1, ISSN (Online) 2300-7443, DOI: 10.2478/coma-2014-0002, July 2014
• Positive metric currents and holomorphic chains in Hilbert spaces, arXiv:1207.5244v1 [math.CV], (to appear inRevista Matem´atica Iberoamericana)
• (with V. Magnani and J. Mal´y)A low rank property and nonexistence of higher dimen-sional horizontal Sobolev sets, arXiv:1212.1563 [math.AP] (to appear in The Journal of Geometric Analysis), DOI: 10.1007/s12220-014-9478-1
• (with G. Tomassini) Transversally pseudoconvex semiholomorphic foliations (to ap-pear inAtti Accad. Naz. Lincei Rend. Lincei Mat. Appl.)
• (with G. Tomassini) 1-complete semiholomorphic foliations, arXiv:1404.6826 [ma-th.CV] (to appear inTransactions of the American Mathematical Society)
• (with C. Mantegazza and M. Rimoldi)The Cotton tensor and the Ricci Flow, http://cvgmt.sns.it/paper/1809/(submitted)
• (with G. Catino and L. Mazzieri)Rigidity of gradient Einstein shrinkers, arXiv:1307.3131 [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 pro-blem. At the present time, only very partial results appear in literature and I’ve been
working, together with G. Tomassini and Z. Slodkowski, at the classification of wea-kly 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 set-tings; 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 ex-tensions 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 be-havior 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 Lp estimates, one of the main directions of research being a development of a theory
´
a 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).
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.
