## Università degli Studi di Padova## Dipartimento di Matematica Tullio Levi-Civita## Home Page of Giovanna Carnovale |

Giovanna Carnovale

Position: Professore Ordinario di Algebra

Address:

Dipartimento di Matematica Tullio Levi-Civita

Università degli Studi di Padova

Via Trieste 63

35121 Padova

Italy

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.

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

Per

sarà concordato in aula.

Per ** Representation Theory of groups **:

see the course webpage.

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

Racks

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). arXiv:2301.03361, submitted.

40. F. Ambrosio, G. Carnovale, F. Esposito, A parametrization of sheets of conjugacy classes in bad characteristic, arXiv:2208.08418, to appear in 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, arXiv:2005.07599, submitted.

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.

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.