Università degli Studi di Padova

Dipartimento di Matematica Tullio Levi-Civita

Home Page of Giovanna Carnovale

Giovanna Carnovale
Position: Professore Ordinario di Algebra

Dipartimento di Matematica Tullio Levi-Civita
Università degli Studi di Padova
Via Trieste 63
35121 Padova
phone: +39-049-8271354
office: 625 (6th floor, corridor CD)
e-mail: carnoval"at"math.unipd.it
Messaggi relativi ai Circoli Matematici da parte dei genitori devono essere inviati ESCLUSIVAMENTE alla casella dedicata: circoli"at"math.unipd.it e NON al mio indirizzo professionale personale. Ringrazio in anticipo per la collaborazione.

Something about me (you never know what people are curious of)
I got my degree in Mathematics in Rome, la Sapienza in 1993, spending my fourth year in Utrecht (NL) as an Erasmus exchange student. My thesis was on coalgebras over the ring of integers. Then I participated in the Master Class on Algebraic Lie Theory and Hypergeometric Functions in the Netherlands, where I also received my PhD in 1999 studying a quantum analogue of Fourier transform. My final advisor was Tom Koornwinder. At the same time I did volunteer work for the Tussenvoorziening and had related training. After spending a few months at Cergy-Pontoise and Paris VI, I moved to Antwerp where I learnt about the Brauer group of Hopf algebras and of braided categories. Shortly after I moved back to Rome, Tor Vergata and in 2001, to Padova where I am professor in Algebra since december 2020. At present I mainly work on algebraic and geometric properties of conjugacy classes in reductive algebraic groups (key example GL(V)) with some digressions in finite groups of Lie type, and an eye to applications in Hopf algebra theory and Representation Theory.

[ Outreach (Italian)| Teaching (mostly in italian) | Research and Publications| Events ]

Outreach activities/ Terza Missione (Italian)

Ho collaborato e collaboro all'organizzazione di questi eventi di divulgazione


Circoli Matematici

Didattica (Teaching)

A.A. 2013-2014:

Ricevimento studenti e pagine dei corsi (office hours + courses home pages):
Fondamenti di Algebra Lineare e Geometria per il Corso di Laurea in Ingengeria Meccanica (matricole pari):
sarà concordato in aula.

Per Representation Theory of groups :
see the course webpage.

Link ai Corsi degli A.A. passati

Research and Publications

Research Interests

Deformation and quantization of algebras,
Hopf algebras and quantum groups,
Brauer groups of braided monoidal categories
Representation theory of Lie algebras, quantum groups, algebraic groups
Conjugacy classes and twisted conjugacy classes in algebraic groups and finite groups of Lie type
Spherical varieties
Surfaces isogenous to a product of curves

Research publications

41. N. Andruskiewitsch; G. Carnovale; G. A. García, Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type VII. Semisimple classes in PSL(n,q) and PSp(2n,q), to appear in Journal of Algebra

40. F. Ambrosio, G. Carnovale, F. Esposito, A parametrization of sheets of conjugacy classes in bad characteristic, Canadian Mathematical Bulletin, First View DOI: https://doi.org/10.4153/S0008439523000097.

39. G. Carnovale, J. Cuadra, E. Masut, Non-existence of integral Hopf orders for twists of several simple groups of Lie type, arXiv:2108.12324, accepted for publication in Publicacions Matemàtiques

38. G. Carnovale, F. Esposito, A. Santi, On Jordan classes for Vinberg's theta-groups, Transformation Groups, online 2021, DOI 10.1007/s00031-021-09675-8.

37. F. Ambrosio, G. Carnovale, F. Esposito, L. Topley, Universal filtered quantizations of nilpotent Slodowy slices, to appear in Journal of Noncommutative Geomtry.

36. G. Carnovale, F. Esposito, P. Fiebig, Localization of IC-complexes on Kashiwara's flag scheme and representations of Kac-Moody algebras, Indagationes Mathematicae, Springer memorial volume, https://doi.org/10.1016/j.indag.2021.06.008, online 2021.

35. F. Ambrosio, G. Carnovale, F. Esposito, Local geometry of Jordan classes in semisimple algebraic groups, 2019, Journal of the London Mathematical Society, https://doi.org/10.1112/jlms.12385

34. G. Carnovale, Lusztig's strata are locally closed, Archiv der Mathematik, 115, 23-26 (2020), DOI :10.1007/s00013-020-01448-1.

33. G. Carnovale; M. Costantini, Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type VI. Suzuki and Ree groups, to appear in Journal of Pure and Applied Algebra, 225(4), 2021, 106568, doi:10.1016/j.jpaa.2020.106568

32. N. Andruskiewitsch; G. Carnovale; G. A. García, Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type V. Mixed classes in Chevalley and Steinberg groups, Manuscripta Math. (2020), doi:10.1007/s00229-020-01248-5

31. G. Carnovale; F. Esposito, Affine hyperplane arrangements and Jordan classes, Journal of Combinatorial Algebra 4(4), 397-446, (2020), DOI: 10.4171/JCA/48

30. G. Carnovale; F. Esposito, Quotients for sheets of conjugacy classes, in ``Representations and Nilpotent Orbits of Lie Algebraic Systems: In Honour of the 75th Birthday of Tony Joseph'', Progress in Mathematics, Birkhäuser,(2019).

29. N. Andruskiewitsch; G. Carnovale; G. A. García, Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type IV. Unipotent classes in Chevalley and Steinberg groups, Algebras and Representation Theory, 23(3), 621-655, (2020) https://doi.org/10.1007/s10468-019-09868-6

28. G. Carnovale; I. I. Simion, On small modules for quantum groups at roots of unity, Bollettino dell'Unione Matematica Italiana 10(1), 99-112, (2017).

27. N. Andruskiewitsch; G. Carnovale; G. A. García, Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type III. Semisimple classes in PSL(n,q), Revista Matemática Iberoamericana, 33(3), 995-1024 (2017).

26. G. Carnovale; A. García Iglesias, θ-semisimple twisted conjugacy classes of type D in PSL(n,q), Journal of Lie Theory 26(1), 193-218 (2016).

25. G. Carnovale; F. Esposito, A Katsylo theorem for sheets of spherical conjugacy classes, arXiv:1501.04534, Representation Theory, 19, 263-280 (2015).

24. N. Andruskiewitsch; G. Carnovale; G. A. García, Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type II. Unipotent classes in the symplectic groups, Communications in Contemporary Mathematics 18(4), 35pp, (2016).

23. N. Andruskiewitsch; G. Carnovale; G. A. García, Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type I. Non-semisimple classes in PSL(n,q), Journal of Algebra 442, 36--65 (2015).

22. G. Carnovale, Lusztig's partition and sheets, with an appendix by M. Bulois, Mathematical Research Letters, 22(3), 645-664, (2015).

21. G. Carnovale; M. Costantini, On Lusztig's map for spherical unipotent conjugacy classes, Bulletin of the London Mathematical Society 45(6), (2013), 1163-1170 doi: 10.1112/blms/bdt048

20. G. Carnovale; Induced conjugacy classes and Induced U_e(G)-modules, Contemp. Math. 585 (2013), 199-211.

19. G. Carnovale; On spherical twisted conjugacy classes, Transformation Groups 17(3), (2012), 615-637.

18. G. Carnovale; F. Esposito, On sheets of conjugacy classes in good characteristic, International Mathematics Research Notices; doi: 10.1093/imrn/rnr047, 2012(4) (2012), 810-828.

17. G. Carnovale; J. Cuadra, On the subgroup structure of the full Brauer group of Sweedler Hopf algebra, Israel Journal of Mathematics 183 (2011) 61--92.

16. G. Carnovale, A classification of spherical conjugacy classes in positive characteristic, arXiv:0811.2641v1, Pacific Journal of Mathematics 245 no.1 (2010), 25-45.

15. G. Carnovale, Spherical conjugacy classes and Bruhat decomposition, preprint arXiv:0808.1818v2, Ann. Inst. Fourier (Grenoble) 59 no. 6 (2009), 2329-2357.

14. G. Carnovale; F. Polizzi, The classification of surfaces of general type with p_g=q=1 isogenous to a product of curves , Adv. Geom. 9 (2009) , no. 2, 233-256.

13. G. Carnovale, Spherical conjugacy classes and involutions in the Weyl group , Math. Z. 260 (2008), no. 1, 1-23.
An addendum rectifying the use of an inexact reference and terminology

12. G. Carnovale, The Brauer group of modified supergroup algebras, J. Algebra 305 (2006), 993-1036.

11. G. Carnovale, When is a cleft extension H-Azumaya? Algebr. Represent. Theory 9 (2006), no. 1, 99-120.

10. J. Bichon; G. Carnovale, Lazy cohomology: an analogue of the Schur multiplier for arbitrary Hopf algebras. J. Pure Appl. Algebra 204 (2006) no. 3, 627-665.

9. N. Cantarini; G. Carnovale; M. Costantini, Spherical orbits and representations of U_e(g). Transform. Groups 10 (2005), no. 1, 29-62.

8. G. Carnovale; J. Cuadra, Cocycle twisting of E(n)-module algebras and applications to the Brauer group. K-Theory 33 (2004), no. 3, 251-276.

7. G. Carnovale; J.Cuadra, The Brauer group BM(k, D_n,R_z) of the dihedral group. Glasgow Math. J. 46 (2004), 239-257.

6. G. Carnovale; J. Cuadra, The Brauer group of some quasitriangular Hopf algebras. J. Algebra 259 (2003), no. 2, 512-532.

5. G. Carnovale, On the q-convolution on the line. Constr. Approx. 18 (2002), no. 3, 309-341.

4. G. Carnovale, Some isomorphisms for the Brauer groups of a Hopf algebra. Comm. Algebra 29 (2001), no. 11, 5291-5305.

3. G. Carnovale; T. H. Koornwinder, A q-analogue of convolution on the line. Methods Appl. Anal. 7 (2000), no. 4, 705-726.

2. G. Carnovale, On the braided Fourier transform on the n-dimensional quantum space. J. Math. Phys 40 (1999), no. 11, 5972-5997.

1. G. Carnovale, Quasidiagonal solutions of the Yang-Baxter equation, quantum groups and quantum super groups. Acta Appl. Math. 53 (1998), 187-228.

Some future and past events:

Quantum 60, december 10-14, 2018, Córdoba, Argentina.

Algebraic Combinatorics in Ancona, june 13-15, 2018.

Workshop Tensor categories, Hopf algebras and quantum groups, Marburg, January 22-26, 2018.

Symmetric spaces and their generalisations, III , celebrating Dmitri Panuyshev's 60th birthday, 26-29 september 2017, Levico Terme.

Mini-workshop on on Lie theory, representation theory and algebraic groups, 11-14 september 2017, Manchester.

Algebraic Modes of Representations. The canicular days, july 16-18, 2017, Weizmann Institute of Science.
Algebraic Modes of Representations and Nilpotent Orbits. The canicular days, july 19-23, 2017, University of Haifa.

Nilpotent orbits and representation theory, june 13-16, 2016, Scuola Normale Superiore, Pisa.

Workshop on Hopf Algebras and Related Topics, Turin, 21-22 January 2016.

Special period: Perspectives in Lie theory december 2014-february 2015 at Centro de Giorgi, Pisa (with extra workshops in Cortona and Rome).

Representations of Algebraic Groups and Related Objects September 08 - 12, 2014, Jena (Germany).

Symmetric Spaces and their Generalisations, II Levico Terme, june 25-29, 2012.

Hopf algebras and Tensor Categories, University of Almerìa (Spain), july 4-8, 2011.

Quantum Groups, Clermont-Ferrand August 30-September 3, 2010.

Representation Theory days in Zurich ETH Zurich, november. 27-29 2009.

B-stable ideals and nilpotent orbits Rome, INdAM, october 8-12, 2007.

Una giornata di Algebra a Roma: a conference in memory of Olivia Rossi Doria La Sapienza, 27 september 2007.