MOV-KNOT   30 October 2018   MOV-KNOT

PERSONAL DATA AND EDUCATION

Personal data:   born in Roma (ITALY) on February 10th, 1968; living there. Married.

Present position:   associate professor of Algebra at the University "Tor Vergata" (Roma, ITALY), faculty of Sciences, department of Mathematics, since November 1st, 2005.
    Qualified as Full Professor of Geometry and Algebra since November 30th, 2017.
    Previously, assistant professor of Algebra at the same institution, from November 1st, 1998, to October 31st, 2005.

Education:
    May 21st, 1991: Laurea in Matematica ( = Master Degree in Mathematics) at the University "La Sapienza" (Roma, ITALY), advisor prof. Claudio Procesi;
    November 5th, 1996: Dottorato di Ricerca in Matematica ( = Ph. D. in Mathematics), at the University "La Sapienza" (Roma, ITALY), advisor prof. Claudio Procesi;

Qualified as Full Professor of Geometry and Algebra since November 30th, 2017   -   see here
Qualified in the class of "Professeur des Universités", Section 25 - Mathématiques, in France, since February 3rd, 2010   -   No of qualification 10125203688

Known Languages:   Italian (native), English (fluent), French (fluent), Spanish (basic).

Fellowships and Grants:





TEACHING ACTIVITY

    Academic years 1998-today:   courses of Algebra, of Geometry and of general Mathematics (for students in Mathematics, in Physics, in Computer Science, in Engineering, in Biology at the University of Rome "Tor Vergata" (Rome, ITALY).
    Academic year 1996-97:   undergraduate course of Analisi Matematica I ( = Calculus 1), for the lower degree in Ingegneria Elettrica (=Electric Engineering), University of "La Sapienza" (Rome, ITALY).





SCIENTIFIC ACTIVITY


Research main guidelines

    My scientific activity till now has been centered around (algebraic) representation theory, Lie theories and their quantization. Within this very broad framework, my research work has focused in particular upon the following topics (the numbers in square brackets below refer to the subsequent list of publications):
  - Algebraic Groups, Representation Theory and related topics: The Schur-Brauer-Weyl duality (for orthogonal and symplectic groups) and the Brauer algebra: see [2], [5], [26] - Algebraic supergroups of special classes: classical type, see [29], [30], [32], [33] and [41]; Cartan type, see [31] and [37] - Real forms of complex supergroups, see [43] - Special features of (general) supergroups: see [36] and [39].
  - Quantum Groups: Quantum universal enveloping algebras and quantum function algebras, their interrelations, structure theory for special classes, presentations, etc.: see [0], [3], [4], [6], [7], [9], [11], [12], [19], [22], [23], [24], [25], [40], [42], [E1] and [E2] - R-matrices (and generalizations) for quantum groups: see [1], [8], [10], [13] and [14] - Quantum homogeneous spaces: see [18], [21], [27], [28] and [35] - Quantum groupoids (=quantizations of bialgebroids): see [34].
  - Hopf Algebras and related structures: Canonical filtrations in Hopf algebras and related graded structures: see [15], [16] and [17] - Quasitriangular structures and generalizations: see [1], [8], [10], [13] and [14]. - Generalizations of Hopf algebras (quasi-Hopf algebras, Hopf superalgebras, bialgebroids, etc.): see [20], [29], [30], [31], [32], [33], [34], [36], [37], [38], [41] and [43].

    For further details, you can read a more complete report (html, pdf) on my work.

Collaborations

These are the people with whom most I work or I used to work:

    Sophie CHEMLA (Paris 7 "Pierre et Marie Curie")   -   Nicola CICCOLI (Perugia)   -   Benjamin ENRIQUEZ (Strasbourg)   -   Rita FIORESI (Bologna)   -   Gastón Andrés GARCÍA (Cordoba / La Falta - Argentina)   -   Gilles HALBOUT (Montpellier 2)   -   Kenji IOHARA (Lyon 1 "Claude Bernard")   -   Niels KOWALZIG (Roma 1 "Sapienza")   -   Paolo PAPI (Roma 1 "Sapienza")   -   Zoran RAKIC (Roma "La Sapienza")


Works in progress



Preprints



Journal articles, Proceedings, etc.


Unpublished essays


Reviews

    No. 77 reviews of books and scientific papers - among which, one Featured Review - for Mathematical Reviews (American Mathematical Society ed.), on the following topics:

    Classical invariant theory and related problems - Linear and multilinear algebra: matrix theory - Lie algebras, Lie bialgebras, universal enveloping algebras and their representations - monoidal, symmetric, braided categories - Coxeter groups, permutation groups, algebraic groups, Lie groups, Lie-Poisson groups and their representations - Hamiltonian systems of finite and infinite dimension, infinite dimensional Poisson varieties - Quantum groups, groups and algebras in quantum theory, quantum mechanics and the problem of quantization - coalgebras, bialgebras, Hopf algebras and generalisations.




Invited Talks (selection)

  • March 2018: "Deformations of quantum groups, their semiclassical limit and specialization at roots of 1", in the workshop "A day in the life of Pi" - Perugia (Italy);
  • October 2017: "From super Harish-Chandra pairs to Lie supergroups", in the workshop "A Lie Day in Bologna, 2017" - Bologna (Italy);
  • March 2017: "Una introducción a la Supergeometría", as Colloquium at the Departamento de Matemática de la Facultad de Ciencias Exactas of the Universidad Nacional de La Plata (Argentine);
  • March 2016: "Supergroupes vs. (super)couples de Harish-Chandra: une nouvelle équivalence", within the seminar "Théorie des Nombres" at the Institut de Mathématiques de Bordeaux, Bordeaux (France);
  • September 2014: "From super Harish-Chandra pairs to affine supergroups", in the international congress "Representations of Algebraic Groups and Related Objects (AlgDar 2014)", Jena (Germany);
  • May 2014: "Affine supergroups and super Harish-Chandra pairs", in the "XVIII Geometrical Seminar", Vrnjacka Banja (Serbia);
  • December 2012: "From simple Lie superalgebras to algebraic supergroups", International Workshop on "Lie Superalgebras", INdAM, Roma (Italy);
  • June 2012: "Supergroupes algébriques associés aux superalgèbres de Lie de type Cartan", Séminaire d'Algèbre - Institut "Henri Poincaré", Paris (France);
  • May 2012: "Algebraic supergroups associated with simple Lie superalgebras - I+II", Facultad de Matemática, Astronomia y Física - Universidad Nacional de Córdoba (Argentina);
  • September 2011: "Algebraic supergroups associated to simple Lie superalgebras", in the Minisymposium "Representation theory of Lie superalgebras" - Köln (Germany);
  • May 2011: "Supergroupes algébriques associés aux superalgèbres de Lie simples", Séminaire d'Algèbre - Institut "Camille Jordan", Université de Lyon 1 (France);
  • May 2011: "Quantification d'éspaces projectifs homogènes (et applications)", Séminaire d'Algèbre - Institut "Henri Poincaré", Paris (France);
  • June 2010: "Supergroupes de Chevalley", Colloque "Solstice d'été 2010", Institut de Mathématiques de Jussieu - Université de Paris 6 & 7 (France);
  • May 2010: "Supergroupes de Chevalley", Journées d'Algèbre à Dijon, Institut de Mathématiques de Bourgogne - Dijon (France);
  • June 2009: "Supergroupes de Chevalley", Séminaire sur les algèbres enveloppantes, Institut de Mathématiques de Jussieu - Université de Paris 6 & 7 (France);
  • June 2009: "Quantification et dualité de Poisson", Journée Groupes Quantiques et Géometrie de Possion, Institut Henry Poincaré - Paris (France);
  • May 2009: "Le radical des algèbres de Brauer", Séminaire sur les algèbres enveloppantes, Institut de Mathématiques de Jussieu - Université de Paris 6 & 7 (France);
  • July 2008: "Quantization of Projective Homogeneous Spaces and Duality Principle", in the ECM satellite Conference "Noncommutative Structures in Mathematics and Physics", Brussels (Belgium);
  • July 2008: "Commuting actions - a tale of two algebras", mini-course for the SOCRATES Intensive Programme GAMAP "Geometric & Algebraic Methods with Applications in Physics", University of Antwerp (Belgium);
  • August 2007: "The global quantum duality principle", in the workshop "Quantum Groups and Noncommutative Geometry", Max Planck Institute for Mathematics - Bonn (Germany);
  • September 2006: "From Hopf algebras to Poisson geometrical symmetries", in the conference "New techniques in Hopf algebras and graded ring theory", Brussels (Belgium);
  • September 2006: "Quantum groups and Hopf algebras", mini-course for the SOCRATES Intensive Programme GAMAP "Noncommutative Algebra, Representation Theory, Noncommutative Geometry", University of Antwerp (Belgium);
  • September 2006: "The global quantum duality principle", in the ICM satellite Conference "Non Commutative Algebra", Granada (Spain);
  • June 2005: "A quantum duality principle for coisotropic subgroups and Poisson quotients", in the International Workshop "Contemporary Geometry and Related Topics", Belgrade (Serbia and Montenegro);
  • September 2004: "Poisson quotients, coisotropic subgroups, and quantizations: a generalized quantum duality principle", Mathematics Institute of SANU, Belgrade (Serbia and Montenegro);
  • May 2003: "A Galois correspondence theorem for quantum groups", in the Miniworkshop "Azioni di gruppi e dintorni", Tor Vergata - Roma (Italy);
  • July 2002: "The quantum duality principle", short course for the summer school "Rencontres Mathématiques de Glanon - 6ème édition", Glanon (France);
  • May 2002: "From quantum symmetries to classical symmetries: a Galois' type correspondence theorem for Hopf algebras", in the International Workshop "Contemporary Geometry and Related Topics", Belgrade (Yugoslavia);
  • March 2002: "Le principe de dualité quantique global", University of Strasbourg (France);
  • June 2001: "The global quantum duality principle", in the 10th International Colloquium "Quantum Groups and Integrable Systems", Prague (Czech Republic);
  • April 2000: "Principio di dualità quantico e applicazioni", in the Workshop on "Gruppi Quantici e Geometria della Quantizzazione", Perugia (Italy);
  • May 1998: "Intrecciamenti per gruppi di Poisson con duale quasitriangolare", University of Ancona (Italy);
  • May 1997: "A PBW basis for Lusztig's form of untwisted affine quantum groups", in the International Conference on "Algebraic groups and representations", Ascona (Switzerland);
  • February 1997: "Interpretation géométrique de la R-matrice pour les groupes quantiques à une racine de l'unitè", University of Strasbourg (Francia);
  • November 1996: "Significato geometrico della R-matrice per gruppi quantici alle radici dell'unità", University of "Tor Vergata", Roma (Italy);
  • August 1995: "New quantum groups associated with Poisson groups", in the summer school Euroconference in Mathematics on Crete on "Algebraic transformation groups and invariant theory", Anogia (Crete, Greece).




  • Visiting periods

  • March 8th-18th, 2017:   Departamento de Matemática de la Facultad de Ciencias Exactas, Universidad Nacional de La Plata   -   La Plata (Argentina);
  • March 10th-12th, 2016:   Institut de Mathématiques de Bordeaux   -   Bordeaux (Francia);
  • June 17th-30th, 2012:   Institut de Mathématiques de Jussieu / Université Paris 6   -   Paris (France);
  • April 22nd - May 14th, 2012:   Facultad de Matemática, Astronomia y Física, Universidad Nacional de Córdoba   -   Córdoba (Argentina);
  • May 26th - June 2nd, 2011:   Institut "Camille Jordan", Université de Lyon 1   -   Lyon (France);
  • April 26th - May 26th, 2011:   Institut de Hautes Études Scientifiques   -   Bures-sur-Yvette (France);
  • April 15th - June 8th 2009:   Institut de Mathématiques de Jussieu   -   Paris (France);
  • March 2009:   Isaac Newton Institute   -   Cambridge (United Kingdom);
  • July 2008:   Faculty of Mathematics and Computer Sciences, University of Antwerp   -   Antwerp (Belgium);
  • January 2008:   Department of Mathematics, University of California at Los Angeles   -   Los Angeles, California (U.S.A.);
  • August 2007:   Max-Planck-Institut fur Mathematik   -   Bonn (Germany);
  • September 2006:   Faculty of Mathematics and Computer Sciences, University of Antwerp   -   Antwerp (Belgium);
  • June 2005:   Faculty of Mathematics, University of Belgrade   -   Belgrade (Yugoslavia/Serbia);
  • September 2004:   Faculty of Mathematics, University of Belgrade   -   Belgrade (Yugoslavia/Serbia);
  • June 2003:   Institut de Recherches Mathématiques Avancées, Université "Louis Pasteur"   -   Strasbourg (France);
  • March 2003:   Institut de Recherches Mathématiques Avancées, Université "Louis Pasteur"   -   Strasbourg (France);
  • May 2002:   Faculty of Mathematics, University of Belgrade   -   Belgrade (Yugoslavia/Serbia);
  • March 2002:   Institut de Recherches Mathématiques Avancées, Université "Louis Pasteur"   -   Strasbourg (France);
  • January 2002:   Institut de Recherches Mathématiques Avancées, Université "Louis Pasteur"   -   Strasbourg (France);
  • March 2001:   Institut de Recherches Mathématiques Avancées, Université "Louis Pasteur"   -   Strasbourg (France);
  • January 2001:   Faculty of Mathematics, University of Belgrade   -   Belgrade (Yugoslavia/Serbia);
  • September 1999:   Institut de Recherches Mathématiques Avancées, Université "Louis Pasteur"   -   Strasbourg (France);
  • January 1997 - February 1998:   Institut de Recherches Mathématiques Avancées, Université "Louis Pasteur"   -   Strasbourg (France);
  • June-July 1996:   Institut of Mathematics, University of Basel   -   Basel (Switzerland);




  • Further scientific activities

  • since December 2016:   member of the Editorial Board of Matematicki Vesnik;
  • since December 2016:   referee for Advances in Pure Mathematics;
  • since December 2015:   referee for Algebras and Representation Theory;
  • since April 2015:   referee for Discrete Mathematics;
  • since June 2013:   referee for Transactions of the American Mathematical Society;
  • since December 2010:   referee for Transformation Groups;
  • since October 2010:   referee for Glasgow Mathematical Journal;
  • since September 2009:   member of the Editorial Board of Le Matematiche;
  • since October 2007:   referee for International Mathematics Research Notices;
  • May 2006:   organizer of the conference "Lie days in Martina Franca" - Martina Franca, Italy (program);
  • since January 2005:   referee for Journal of Geometry and Physics;
  • April 2004:   organizer of the workshop "The interplay of representation theory, Poisson geometry and quantization", University of "Tor Vergata", Roma, Italy (program);
  • since May 2003:   referee for Advances in Mathematics;
  • since May 2003:   referee for Letters in Mathematical Physics;
  • May 2001:   organizer of the workshop "Gruppi Quantici e dintorni", University of "Tor Vergata", Roma, Italy (program);
  • since October 1998:   organizer of the permanent seminar "Young Algebra Seminar", at the department of Mathematics of the University of "Tor Vergata", Roma (Italy);
  • since March 1997:   referee for Journal of Algebra;
  • from June 1998 to May 2008:   reviewer for Mathematical Reviews, edited by the American Mathematical Society.


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        Last updated:   30 October 2018   -   Fabio Gavarini