Foto del docente

Nicoletta Cantarini

Professor

Department of Mathematics

Academic discipline: MAT/02 Algebra

Curriculum vitae

 

Name: Nicoletta Cantarini
Date of birth: January 19th 1971
Affiliation: Dipartimento di Matematica, Universita di Bologna, Piazza di Porta San Donato 5, Bologna, Italy
Telephone: +39 051 2094442
Fax number: +39 051 2094490
e-mail: nicoletta.cantarini@unibo.it
Qualications:
- 1993: Degree in Mathematics (full-honours).
- 1998: PhD in Mathematics (University of Pisa, Italy).
Present position: Full Professor of Algebra at the University of Bologna, Italy.
Main research interests
- Lie algebras and superalgebras.
- Poisson algebras.
- Jordan algebras.
- Quantum groups and their representations.
- Representations of Lie superalgebras.
- n-algebras and their applications to physics.
Studies and career
1993 Graduated with honours in Mathematics at the University of Bologna. First degree thesis: Metodi
geometrici della meccanica quantistica. Advisor: Prof. R. Giachetti.
1994-1998 Ph. D. student at the Department of Mathematics of the University of Pisa. Ph.D. Thesis:
Representation Theory of Quantized Enveloping Algebras at the Roots of Unity. Advisor: Professor
C. De Concini.
1998 INdAM (Istituto Nazionale di Alta Matematica) Senior grant at the Department of Mathematics
of the University La Sapienza of Rome.
1998 SISSA (Scuola Internazionale Superiore di Studi Avanzati) post-doc fellowship.
1998 Won the "Francesco Severi" award for young mathematicians.
1998-1999 Post-doc grant by Italian CNR at the Ecole Normale Superieure, Paris, under the supervi-
sion of Professor V.G. Kac.
1999 Post-doc grant at the Department of Mathematics, University of Pisa.
2000 Research position at the Department of Mathematics, University of Pisa.
2000-2006 Tenured Assistant Professor at the Department of Mathematics, University of Padova.
2006-2011 Associate Professor of Algebra at the Department of Mathematics, University of Padova.
2011- 2014 Associate Professor of Algebra at the Department of Mathematics, University of Bologna.
2014- Full Professor in Algebra at the Department of Mathematics, University of Bologna.

Visits to research Institutes
2000 In November was a visiting guest at MIT, Cambridge, MA.
2001 In April was a visiting guest at the Laboratoire de Mathemtiques Fondamentales of Pierre et
Marie Curie University, Paris, supported by European Socrates Exchange Programme.
2002 In April was a visiting guest at the MSRI, University of California, Berkeley.
2003 In May was a visiting guest at the Department of Mathematics, University "La Sapienza", Rome,
during the program "Moduli, Lie theory, interactions with physics".
2004 In March and April was a visiting guest at MIT, Cambridge (MA).
2004 In June was a visiting guest at the Department of Mathematics, University "La Sapienza", Rome.
2004 In December was a visiting guest at MIT, Cambridge (MA).
2005 In June was a visting guest at the Institut des Hautes Etudes Scientiques (Bures sur Yvette).
2006 In January, March and June was a visting guest at the Institut des Hautes Etudes Scientiques
(Bures sur Yvette).
2007 In December was a visting guest at the Department of Mathematics, University "La Sapienza",
Rome.
2008 In May was a visiting guest at the Department of Mathematics, University "La Sapienza", Rome.
2009 In May was a visiting guest at the Laboratoire de Mathematiques Fondamentales of the University
Pierre et Marie Curie, Paris.
2010 In May was a visiting guest at the Department of Mathematics, University "La Sapienza", Rome.
2011 In January was a visiting guest at the Department of Mathematics, University "La Sapienza",
Rome.
Organizing activities
2002-2003 Was the scientic coordinator of a research project supported by the University of Padova.
Title of the project: Representations of quantized enveloping algebras at the roots of unity.
Has participated in National and International Research Projects. At the moment is taking part to the
2009 Prin Project Spazi di moduli e teoria di Lie (PI: Professor Corrado De Concini) and to the FIRB project
Perspectives in Lie Theory (PI: Prof. A. De Sole).
2005-2006: was an evaluator of the Research Projects for the University of Padova.
Since 2006 is an evaluator for the European Community and participated in the Sixth Framework
Programme.
Coorganized the following conferences: - Una giornata di Algebra a Roma: a conference in memory
of Olivia Rossi Doria, Rome, September 27 2007;
- Symmetries in Mathematics and Physics, Cortona, June 22-28 2008;
- The interplay of Algebra and Geometry, Cortona, June 14-20 2009.
- `Symmetries in Mathematics and Physics 2013', Rio de Janeiro, INPA, 24-28 giugno 2013. -Aspects of Lie Theory, INdAM, Roma, January 7-10 2015.
Was invited speaker at several International conferences among which we list the following:
- Algebras and Representation Theory, University of Warwick, 26-31 maggio 2005;
- Symmetries in Geometry and Physics, Universita di Roma La Sapienza, 14-17 settembre 2005;
- Lie days in Martina Franca, 22-27 maggio 2006;
- Seminar on Enveloping Algebras, Universite de Paris 6, 5 maggio 2007;
- Joint International Meeting UMI - DMV, Perugia, 18-22 giugno 2007;
- Seminario di Algebra e Geometria, Universita di Roma La Sapienza, 31 ottobre 2008;
- Seminaire sur les Algebres Enveloppantes et Theorie des Representations, Laboratoire de
Mathematiques Fondamentales dell'Universita Pierre et Marie Curie, 22 maggio 2009;
- Symmetric spaces and their generalisations, Levico, 14-18 giugno 2010;
- Enveloping Algebras and Geometric Representation Theory, Oberwolfach, 4-10 marzo 2012.
Papers

International Journals
[1] N. Cantarini. Representations of slq(3) at the roots of unity. Rendiconti Lincei: Matematica e Applicazioni, serie IX, vol. VII, no. 4, 201-212 (1996).
[2] N. Cantarini. Mod-p reduction for quantum groups. J. Algebra 202, 357-366 (1998).
[3] N. Cantarini. Spherical orbits and quantized enveloping algebras. Comm. Algebra 27(7), 3439-3458 (1999).
[4] N. Cantarini. The quantized enveloping algebra Uq(sl(n)) at the roots of unity. Comm. Math. Phys. 211, 207-230 (2000).
[5] N. Cantarini. Z-Graded Lie superalgebras of infinite depth and ifinite growth. Annali della Scuola Normale Superiore di Pisa Cl. Sci. 5(1), 545-568 (2002).
[6] N. Cantarini. A classification of Z-graded Lie superalgebras of infinite depth. Journal of Algebra and its Applications 1(4), 425-449 (2002).
[7] N. Cantarini, S.-J. Cheng, V. G. Kac. Errata to "Structure of some Z-graded Lie superalgebras of vector fields", Transformation Groups 9(4), 399-400 (2004).
[8] N. Cantarini, G. Carnovale, M. Costantini. Spherical orbits and representations of U_e(g). Transformation Groups 10(1), 29-62 (2005).
[9] N. Cantarini, V.G. Kac. Infinite dimensional primitive linearly compact Lie superalgebras, Adv. Math., 207(1), 328-419 (2006).
[10] N. Cantarini, V.G. Kac. Automorphisms and forms of simple infinite dimensional linearly compact Lie superalgebras, Int. J. Geom. Methods Mod. Phys. 3(5-6), 845-867 (2006).
[11] N. Cantarini, V.G. Kac. Classification of linearly compact simple Jordan and generalized Poisson superalgebras, J. Algebra 313, 100-124 (2007).
[12] N. Cantarini, V.G. Kac. Classification of linearly compact simple rigid superalgebras. Int. Mat. Res. Not. 2010(17), 3341-3393 (2010).
[13] N. Cantarini, V.G. Kac. Classification of simple linearly compact n-Lie superalgebras. Commun. Math. Phys. 298(3), 833-853 (2010).
[14] N. Cantarini, V.G. Kac. Classification of simple linearly compact N = 6 3-algebras. Transform. Groups 16(3), 649-671 (2011).
[15] N.Cantarini, V.G.Kac. Algebraic vs physical N=6 3-algebras. J. Math. Phys. 55(1) (2014).

[16] N.Cantarini, V.G. Kac. Classification of linearly compact simple Nambu-Poisson algebras. J. Math. Phys. 57, 051701 (2016).

Preprints and other papers
[17] N. Cantarini. Teoria delle rappresentazioni di algebre inviluppanti quantizzate alle radici dell'unita`. Bollettino della Unione Matematica Italiana, Supplemento Tesi di Dottorato (1999).
[18] N. Cantarini. Z-Graded Lie superalgebras. Atti del ciclo di seminari YAS - Young Algebra Seminar, Dipartimento di Matematica, Universita Tor Vergata di Roma (2001).
[19] N. Cantarini. A sketch on the classification of Z-graded Lie Superalgebras. Seminari di Geometria 2001-2004, Univ. Stud. Bologna, 17-33 (2004).
[20] N. Cantarini, V.G. Kac. Representations of the Lie superalgebras E(5,10), in preparation (2016)

PhD Thesis
[20] N. Cantarini. Representation Theory of Quantized Enveloping Algebras at the Roots of Unity. Tesi di dottorato, Universita` di Pisa (1998).

Books
[21] N. Cantarini., B. Chiarellotto. Un Corso di Matematica. Edizioni Progetto, Padova, 2001.

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