Name: Graziano GENTILI
Date and place of birth: 6 April 1955, Fauglia (Pisa) - Italy.
Present position: full professor at the University of Firenze, Italy.
Address: Dipartimento di Matematica e Informatica “U.Dini”, Viale Morgagni 67/A, 50134 Firenze, Italy.
Private Address: via nove febbraio 24, 50129 Firenze, Italy.
Curriculum Studiorum
• 1974 -1978: Undergraduate studies, Scuola Normale Superiore, Pisa, Italy.
• 13 July 1978: Tesi di Laurea ”Di↵erential Geometry on Convex Cones”. Advisor: Prof. Edoardo Vesentini.
• 1979 -1981: Ph.D. student, at ”corso di perfezionamento”, Scuola Normale Superiore, Pisa, Italy.
• 15 July 1981: Tesi di Perfezionamento ”Invariant Riemannian Geometry on Convex Cones”. Advisor: Prof. Edoardo
Vesentini.
Promotions and positions in Italy:
• ”Ricercatore universitario confermato”, Classe di Scienze, Scuola Normale Superiore, Pisa, from 1 August 1980 until
14 May 1987.
• Associate professor, Classe di Matematica, International School for advanced Studies, Trieste, from 15 May 1987
until 31 October 1991.
• Professor, University of Trieste, from 1 November 1991 until 31 October 1994.
• Professor, University of Firenze, from 1 Novembre 1994.
Visits and positions abroad:
• Visiting Assistant Professor at the Department of Mathematics of the University of Maryland at College Park (USA)
during the Spring Semester of 1982, the months of September and October 1984 and November 1985.
• Visiting Faculty at the T.J.Watson Research Center (I.B.M.) at Yorktown Heights, NY (USA), during the Summer
term of 1987, third term 1988 and the month of July 1990.
• Visiting at the Mathematical Institute of the University of Oxford (UK), during the months of July 1988 and June
1990.
• Visiting professor at the Graduate School of the George Mason University, Fairfax, Virginia (USA), during the
month of April 1992.
• Visiting Faculty at the T.J.Watson Research Center (I.B.M.) at Yorktown Heights, NY (USA), during the month
of May 1994.
• Visiting Professor at the Department of Mathematics of the University of Toronto, Ontario (Canada), during the
month of March 1996.
• Professor at the ”Mathematisches Institut” of the University of Erlangen-Nuernberg, Germany, during the Summer
semester 1998.
• Visiting Professor at the Graduate School of the George Mason University, Fairfax, Virginia (USA), during the Fall
semester 2005 and the month of June 2006.
• Short-term Visitor at the Department of Mathematics of the University of Cyprus, during the month of November
2006.
• Visiting Professor at the Department of Mathematics and Computer Science of the Chapman University, Orange,
California (USA), during the months of January and September 2007, January and July 2008, January and July 2009,
January 2010, July 2011, July 2012, June 2013, June 2014.
Congresses and Conferences:
Gentili has been invited to, and has given talks at, many international Congresses and Conferences, since the beginning
of his scientific activity. The participations from the year 2010 are the following:
• Rome, Italy; September 2010; ”INdAM Workshop: Di↵erent Notions of Regularity for Functions of Quaternionic
Variable”. (title of the talk: Rigidity properties of slice regular functions over the quaternions.)
• Ljubliana, Slovenia; February 2011: ”Matematini kolokvij in the year 2011”. (title of the talk: Regular functions of
a quaternionic variable.)
• Moscow, Russia; August 2011: 8th ISAAC Congress (Cli↵ord and quaternion analysis)”. (title of the talk: The
Weierstrass Factorization Theorem for slice regular functions.)
• Roma, February 2012, Accademia Nazionale dei Lincei, ”Con la Mente e con le mani”. (title of the talk: Il taglia e
incolla e la congettura di Poincaré.)
• Roma, November 2012, Accademia Nazionale dei Lincei, ”Con la Mente e con le mani”. (title of the talk: Alcuni
problemi di Teoria dei Giochi.)
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• Cuernavaca, Mexico; January 2013; Instituto de Matemticas UNAM; ”AlbertoFest: Complex Geometry, Dynamical
Systems and Number Theory”. (title of the talk: Regular functions of a quaternionic variable: applications.)
• Pisa, February 2013; Scuola Normale Superiore; ”Varietà reali e complesse: geometria, topologia e analisi armonica”.
(Title of the talk: Funzioni regolari di variabile quaternionica.)
• Lancaster, UK, March 2013; Department of Mathematics and Statistics, Lancaster University. (Title of the talk:
Regular functions of a quaternionic variable and orthogonal complex structures.)
• Krakow, Poland; August 2013: 9th ISAAC Congress (Cli↵ord and quaternion analysis)”. (Title of the talk: Results
of geometric theory of hypercomplex functions on the unit ball of quaternions.)
• Nahariya, Israel; May 2013; ”Complex Analysis and Dynamical Systems, VI”. (Title of the talk: Regular functions
of a quaternionic variable and orthogonal complex structures.)
• Orange, California, Chapman University, November 2013; ”Workshop on Results in Mathematics and Physics
obtained by Methods of Hypercomplex Analysis”. (Title of the talk: Ideals of regular functions of a quaternionic
variable.)
• Bilbao, Spain, July 2014; ”First Joint International Meeting of the Italian and Spanish Mathematical Societies
RSME-SCM -SEMA -SIMAI-UMI”. (Title of the talk: On Quaternionic Tori and their moduli space.)
• Orange, California, Chapman University, October 2014; ”Workshop on Integral transforms, boundary values and
generalized functions”. (Title of the talk: Spherical power expansion and a Mittag-Le✏er theorem for semi-regular
functions.)
• Shanghai, China, East China Normal University, May 2015; ”International Conference on Complex Geometry and
Several Complex Variables”.
Academic titles and Prizes:
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”Diploma di Laurea” in Mathematics.
”Diploma di Licenza” in Mathematics of the Scuola Normale Superiore, Pisa.
”Diploma di Perfezionamento” of the Scuola Normale Superiore, Pisa.
”Luigi Bianchi” Prize 1982.
”Medaglia dell’Accademia delle Scienze detta dei XL per la Matematica per il 2006”.
Main research interests:
Geometric Theory of Holomorphic maps in one and several complex variables. Holomorphic Dynamics and Iteration
Theory. Functional equations. Quaternionic and hypercomplex analysis and geometry. Geometric Modelling, Formal
Proving and applications.
Teaching and research training:
Gentili teaches the Courses of ”Geometria I” and ”Istituzioni di Geometria Superiore” (Corso di Laurea in Matematica)
and gives talks to Ph.D. students. He has taught several PH.D. courses, in 2005 and 2007 on ”Hyperbolic Geometry”.
He has been advisor of approximately 45 ”Tesi di Laurea” in Mathematics, several of which are research oriented. He
has been as well advisor of (or has contributed to) the following Tesi di dottorato:
• F. Vlacci, Iteration theory and commuting holomorphic maps, Sissa, Trieste, 1997.
• B. Visintin, Complex Geodesics in Reinhardt Domains, Sissa, Trieste, 1998.
• F. Bracci, Fixed points of holomorphic mappings, Padova, 2001
• C. Bisi, Iteration Theory, Commuting Holomorphic Maps and Complex Dynamics at the Wol↵ Point, Firenze, 2001
• S. Migliorini, Boundary rigidity results for holomorphic maps, Firenze, 2002
• C. Frosini, Holomorphic dynamics in the complex bidisc, Firenze, 2004
• C. Stoppato, Regular functions of a quaternionic variable, Firenze, 2010
• G. Sarfatti, Elements of Function Theory in the Unit Ball of Quaternions, Firenze, 2013
• I. Vignozzi, Slice regular functions over the quaternions: the Weierstrass Factorization Theorem, Firenze, 2015.
Organizational activities for research training:
• Since 2004: in charge of the scientific agreements between the Dipartimento di Matematica e Informatica ”U.Dini” of
the University of Firenze and various foreign institutions, including the Mathematics Department of the University of
California at Los Angeles and the Instituto de Matematicas, Universidad National Autonoma de Mexico at Cuernavaca.
• Since 1995: member of the Collegio Docenti of the Dottorato in Matematica of the University of Firenze.
• 2010 Member of the Scientific Committee of the ”INdAM Workshop on Di↵erent Notions of Regularity for Functions
of Quaternionic Variable”, Roma, 13 - 17 September 2010.
• 2008 Director (with G. Patrizio e J. Guenot) of the C.I.M.E. course ”Holomorphic Dynamical Systems”, July 7 12, 2008 - Cetraro (Cosenza).
• 1994-2004: Director of the Scuola Matematica Interuniversitaria, and since then member of the Consiglio Direttivo of
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the Scuola. The Scuola Matematica Interuniversitaria organizes Summer Courses of Mathematics at a post-graduate
level, addressed to young graduate students, both from Italy and from abroad, and prepares them for attendance to
Ph.D. courses, Dottorati di ricerca in Italy, post-graduate Schools and research activities in general.
• In the year 2006: Founder - and since then member of the Governing Board - of the Consorzio Interuniversitario per
l’Alta Formazione in Matematica. Members of this Consorzio are: Scuola Normale Superiore (Pisa), SISSA (Trieste),
Istituto Nazionale di Alta Matematica “F. Severi” (Rome), Università di Perugia, Scuola Matematica Interuniversitaria
(Firenze).
Research Direction and Coordination:
• Currently Director of ”Gruppo Nazionale per le Strutture Algebriche, Geometriche e Applicazioni”(GNSAGA) of
the Istituto Nazionale di Alta Matematica ”F. Severi”, Roma (INdAM) (2013-2017).
• Currently coordinator of the Firenze unit of the PRIN2010-2011 Research Project entitled ”Real and complex
manifolds: geometry, topology and harmonic analysis”.
• National coordinator of the FIRB research project entitled ”Dynamics and group actions in complex domains and
manifolds”, financed in the years 2003-2006.
• Coordinator of the Trieste unit of the PRIN Research Project entitled ”Real and complex geometry”, 1991-1994.
• Coordinator of the Firenze unit of the PRIN Research Project entitled ”Real and complex geometry of manifolds”,
1995-1996.
Research Evaluation and Peer reviewing:
• 2014/2015 Member of the Selection Committee for the Evaluation of SIR 2014 Projects in the ERC Sector PE.
• 2012 Member of GEV01 (Mathematics and Computer Science) for the VQR 2004-2010, National Agency for the
Evaluation of Universities and Research Institutes in Italy (ANVUR).
• 2011 President of the Panel INdAM-COFUND for the attribution of INdAM European Research Fellowships.
• Referee for International Journals and for the evaluation of FIRB and PRIN Projects.
Editorial activities:
Currently:
• Editor-in-Chief of the journal
”Annali di Matematica Pura ed Applicata”.
• Member of the Editorial Board of the following Journals:
”Advances in Geometry”
”Complex Manifolds”
Previously:
• 1992 -1997: Editor in Chief of the Journal ”Rendiconti dell’Istituto di Matematica dell’Università degli Studi di
Trieste”.
• 1998 -2008: Member of the Editorial Board of the Journal ”Rendiconti dell’Istituto di Matematica dell’Università
degli Studi di Trieste”.
• 2006 -2012: Member of the Editorial Board of the Journal ”Bollettino dell’Unione Matematica Italiana”.
Services:
Currently:
• Coordinator of the Firenze -Perugia -INdAM Ph.D. Program in ”Mathematics, Computer Science, Statistics”, from
the year 2013.
• Member of the ”Ethics Committee” of the European Mathematical Society since the year 2010;
• Coordinator of an Agreement between UMI and the Massachussets Institute of technology (MIT). This Agreement
organizes positions of ”Visiting Students” at MIT, for selected Italian graduate students that want to do their researches
at MIT for one or more Terms.
Previously:
• 2006 -2012: Vice-President of the Unione Matematica Italiana (UMI).
Languages:
Italian and English
Publications:
For a complete list follow this link:
Publications
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Graziano(Gentili(–(Choice(of((20(publications(
!
Journal(Articles(
[1]! R.! Farouki,! G.! Gentili,! C.! Giannelli,! A.! Sestini,! C.! Stoppato.! Solution! of! a! quadratic!
quaternion! equation! with! mixed! coefficients.! J.! Symbolic! Comput.,! vol.! EE,! pp.! 1E19,!
published!online,!2015.!
!
[2]!!G.!Gentili,!S.!Salamon,!and!C.!Stoppato.!Twistor!transforms!of!quaterE!nionic!functions!
and!orthogonal!complex!structures.!J.!Eur.!Math.!Soc.!(JEMS),!16(11):2323–2353,!2014.!!
[3]!!G.!Gentili!and!C.!Stoppato.!Power!series!and!analyticity!over!the!quaterE!nions.!Math.!
Ann.,!352(1):113–131,!2012.!!
[4]!!G.!Gentili!and!D.!C.!Struppa.!Lower!bounds!for!polynomials!of!a!quaterE!nionic!variable.!
Proc.!Amer.!Math.!Soc.,!140(5):1659–1668,!2012.!!
!
[5]!!G.!Ciolli,!G.!Gentili,!and!M.!Maggesi.!A!certified!proof!of!the!Cartan!fixed!point!theorems.!
J.!Automat.!Reason.,!47(3):319–336,!2011.!!
!
[6]!!F.!Bracci,!G.!Gentili,!and!P.!PoggiECorradini.!Valiron’s!construction!in!higher!dimension.!
Rev.!Mat.!Iberoam.,!26(1):57–76,!2010.!!
[7]!!F.!Colombo,!G.!Gentili,!and!I.!Sabadini.!A!Cauchy!kernel!for!slice!regular!functions.!Ann.!
Global!Anal.!Geom.,!37(4):361–378,!2010.!!
[8]! !C.! Bisi! and! G.! Gentili.! Möbius! transformations! and! the! Poincaré! distance! in! the!
quaternionic!setting.!Indiana!Univ.!Math.!J.,!58(6):2729–2764,!2009.!!
[9]! !F.! Colombo,! G.! Gentili,! I.! Sabadini,! and! D.! Struppa.! Extension! results! for! slice! regular!
functions!of!a!quaternionic!variable.!Adv.!Math.,!222(5):1793–!1808,!2009.!!
!
[10]! !G.! Gentili! and! C.! Stoppato.! The! open! mapping! theorem! for! regular! quaternionic!
functions.!Ann.!Sc.!Norm.!Super.!Pisa!Cl.!Sci.!(5),!8(4):805–815,!2009.!!
!
[11]! !G.! Gentili! and! C.! Stoppato.! Zeros! of! regular! functions! and! polynomials! of! a!
quaternionic!variable.!Michigan!Math.!J.,!56(3):655–667,!2008.!!
!
[12]! G.! Gentili! and! D.! C.! Struppa.! On! the! multiplicity! of! zeroes! of! polynomials! with!
quaternionic!coefficients.!Milan!J.!Math.,!76:15–25,!2008.!
[13]! !G.! Gentili,! D.! C.! Struppa,! and! F.! Vlacci.! The! fundamental! theorem! of! algebra! for!
Hamilton!and!Cayley!numbers.!Math.!Z.,!259(4):895–902,!2008.!!
!
[14]! F.! Colombo,! G.! Gentili,! I.! Sabadini,! and! D.! C.! Struppa.! A! functional! calculus! in! a!
noncommutative!setting.!Electron.!Res.!Announc.!Math.!Sci.,!14:60–68,!2007.!!
!
[15]! !G.! Gentili! and! D.! C.! Struppa.! A! new! theory! of! regular! functions! of! a! quaternionic!
variable.!Adv.!Math.,!216(1):279–301,!2007.!!
!
[16]! G.! Gentili! and! D.! C.! Struppa.! A! new! approach! to! CullenEregular! functions! of! a!
quaternionic!variable.!C.!R.!Math.!Acad.!Sci.!Paris,!342(10):741–744,!2006.!
!
[17]! !F.! Bracci! and! G.! Gentili.! Solving! the! Schröder! equation! at! the! boundary! in! several!
variables.!Michigan!Math.!J.,!53(2):337–356,!2005.!!
!
[18]!!C.!de!Fabritiis!and!G.!Gentili.!On!holomorphic!maps!which!commute!with!hyperbolic!
automorphisms.!Adv.!Math.,!144(2):119–136,!1999.!
[19]! !G.! Gentili.! On! complex! geodesics! of! balanced! convex! domains.! Ann.! Mat.! Pura! Appl.!
(4),!144:113–130,!1986.!!
!
!
A(Monograph(
[20]! G.! Gentili,! C.! Stoppato,! and! D.! C.! Struppa.! Regular! functions! of! a! quaterE! nionic!
variable.!Springer!Monographs!in!Mathematics.!Springer,!Heidelberg,!2013.!
!