Research

Here is my ORCID Research CV and my Ciência Vitae CV

Scientific Interests

Complex Algebraic and Differential Geometry, Moduli Spaces and Character Varieties, Geometric Invariant Theory, Riemann Surfaces, Mathematical-Physics

Research Affiliation

- CMAFcIO - Centro de Matemática, Aplicações Fundamentais e Investigação Operacional, Faculty of Sciences, Univ. Lisbon (Full Member)
- CAMGSD - Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, IST, Univ. Lisboa
- GFMUL - Mathematical Physics Group of the University of Lisbon

International Research Networks

Research Projects

Editorial Boards

Seminar Series

Publications

Scientific Articles:

Character varieties:
  1. C. Florentino and S. Lawton, "Flawed groups and the topology of character varieties", arXiv:2012.08481.
  2. C. Florentino, A. Nozad, J. Silva and A. Zamora, "On Hodge polynomials of singular character varieties", to appear in "Springer Proceedings in Mathematics & Statistics", Proceedings of the Conference ISAAC 2019, Aveiro. Preprint arXiv:2006.14520.
  3. C. Florentino, A. Nozad and A. Zamora, Serre polynomials of SLn- and PGLn-character varieties of free groups", Jour. Geom. & Physics, 161 (2021) 104008 (arXiv:1912.05852 [nath.AG]).
  4. C. Florentino, A. Nozad and A. Zamora, "Generating series for the E-polynomials of GL(n,ℂ)-character varieties", to appear in Math. Nacrichten (arXiv:1902.06837).
  5. C. Florentino and J. Silva, "Hodge-Deligne polynomials of abelian character varieties", to appear in Open Mathematics (Preprint arxiv:1711.07909).
  6. C. Florentino, S. Lawton and D. Ramras, "Homotopy groups of free group character varieties", Annali Sc. Norm. Sup. Pisa, Classe di Scienze, 17 (2017) 143-185.
  7. A. Casimiro, C. Florentino, S. Lawton and A. Oliveira, "Topology of Moduli Spaces of Free Group Representations in Real Reductive Groups", Forum Mathematicum, 28 (2016) 275-294.
  8. A. Casimiro, C. Florentino, S. Lawton, A. Oliveira, "Homotopy type of free group character varieties", Boletim da SPM, Special Issue, 2016, Proceedings of the ENSPM 14.
  9. I. Biswas and C. Florentino, "Character varieties of virtually nilpotent Kähler groups and G-Higgs bundles", Annales de L'Inst. Fourier, 65 (2015) 2601—2612.
  10. C. Florentino and S. Lawton, "Topology of character varieties of abelian groups", Topology and its Applications 173 (2014) 32-58. (Preprint arXiv-math/1301.7616).
  11. I. Biswas, C. Florentino, S. Lawton, M. Logares, "The Topology of Parabolic Character Varieties of Free Groups", Geom. Dedicata 168 (2014) 143-159.
  12. C. Florentino and S. Lawton, "Character Varieties and the Moduli of Quiver Representations", in "In the Tradition of Ahlfors-Bers, VI", Contemporary Mathematics 590, AMS (2013) 9-38. (Preprint arxiv-math/1104.2960)
  13. C. Florentino and S. Lawton, "Singularities of free group character varieties", Pacific J. Math. 260 (2012) 149-179 (arxiv-math/0907.4720).
  14. C. Florentino and S. Lawton, "The topology of moduli spaces of free group representations", Math. Annalen 345 (2009) 453-489. .
Moduli of bundles:
  1. C. Florentino, P. B. Gothen, A. Nozad, "Homotopy Type of Moduli Spaces of G-Higgs Bundles and Reducibility of the Nilpotent Cone", Bull. Sci. Math 150 (2019) 84-101
  2. A. Casimiro, S. Ferreira, C. Florentino, "Principal Schottky Bundles over Riemann surfaces", Geom Dedicata (2018) doi.org/10.1007/s10711-018-0398-2.
  3. I. Biswas and C. Florentino, "Higgs bundles and representation spaces associated to morphisms", Archivum Mathematicum 51 (2015), 191-199.
  4. I. Biswas, C. Florentino, L. Godinho, A. Mandini, "Symplectic form on hyperpolygon spaces", Geom. Dedicata 179, 1 (2015) 187–195.
  5. C. Florentino and T. Ludsteck, "Unipotent Schottky bundles on Riemann surfaces and complex tori", Int. J. of Math., 25 (6) 2014. Preprint arxiv-math/1102.3006.
  6. I. Biswas and C. Florentino, "Commuting elements in reductive groups and Higgs bundles on abelian varieties", J. Algebra, 388 (2013) 194-202.
  7. I. Biswas, C. Florentino, L. Godinho, A. Mandini, "Polygons in Minkowski three space and parabolic Higgs bundles of rank two on CP^1", Transf. Groups 18, (4) (2013), 995-1018.
  8. I. Biswas and C. Florentino, "A remark on "Connections and Higgs fields on a principal bundle"", Ann. Glob. Anal. Geom. 40 (2011) 287-289 (arXiv:1102.4216)
  9. I. Biswas and C. Florentino, "The topology of moduli spaces of group representations: The case of compact surface", Bull. Sci. math. 135 (2011) 395–399.
  10. C. Florentino, "Schottky uniformization and vector bundles over Riemann surfaces" Manuscripta Math. 105, no.1, (2001), 69-83 (preprint math.DG/0104211).
  • Tese de Doutoramento: C. Florentino, "On Schottky vector bundles over Riemann surfaces" (PhD in Pure Mathematics, SUNY at Stony Brook, EUA, 8/1997, supervisionada por L. Takhtajan (reduced format)).
Geometric quantization:
  1. I. Biswas, C. Florentino, J. Mourão, J. P. Nunes, "Quantization of some moduli spaces of parabolic vector bundles on CP^1", Ann. Global Analysis and Geom, 43 (2) (2013), 161-176 (arxiv-math/1111.4838).
  2. T. Baier, C. Florentino, J. Mourão and J. P. Nunes, "Toric Kähler metrics seen from infinity, quantization and compact tropical amoebas", Jour. Diff. Geom. 89 (3) (2011) 411-454 (arxiv-math/0806.0606).
  3. C. Florentino, J. Mourão and J. P. Nunes, "Theta functions, geometric quantization and unitary Schottky bundles", in "The Geometry of Riemann Surfaces and Abelian Varieties", Contemporary Mathematics 397 (2006) 55-72.
  4. C. Florentino, P. Matias, J. Mourão and J. P. Nunes, "On the BKS pairing for Kähler quantizations of the cotangent bundle of a Lie group", J. Funct. Anal. 234 (2006) 180-198.
  5. C. Florentino, P. Matias, J. Mourão and J. P. Nunes, " Geometric quantization, complex structures and the coherent state transform", J. Funct. Anal. 221, no.2 (2005) 303-322. (math.DG/0402313)
  6. C. Florentino, J. Mourão and J. P. Nunes, "Coherent state transforms and Theta Functions", Proc. of Steklov Inst. of Math. 246 (2004) 283-302. (dedicated to A. N. Tyurin).
  7. C. Florentino, J. Mourão and J. P. Nunes, "Coherent state transforms and Vector Bundles on Elliptic Curves" , J. Funct. Anal. 204, no.2 (2003) 355-398. (math.AG/0206269).
  8. C. Florentino, J. Mourão and J. P. Nunes, "Coherent state transforms and Abelian Varieties" , Jour. Funct. Analysis 192, no. 2, (2002) 410-424.
Invariant theory:
  1. A. C. Casimiro and C. Florentino, "Stability of Affine G-varieties and Irreducibility in Reductive Groups", Int. J. Math. 23, (8) (2012), (Preprint arXiv:1110.4236)
  2. C. Florentino, "Simultaneous similarity and triangularization of sets of 2 by 2 matrices", Lin. Alg. and Applications 431 (2009) 1652-1674. (arxiv-math/0809.3032).
  3. C. Florentino, "Invariants of 2 by 2 matrices, irreducible SL(2,C) characters and the Magnus trace map", Geom. Dedicata 121 (2006) 167-186.

Other Articles:

Search my scientific articles in www.arxiv.org

Supervision of PhD Theses:

  • Susana Ferreira, "Schottky principal bundles over comapct Riemann surfaces" (co-orientation by Ana C. Casimiro) 12/9/2014, FCT-Univ. Nova Lisboa.
  • Jaime Silva, "Mixed Hodge Structures of Character Varieties", 30/4/2018, IST, U Lisboa.

Supervision of Master Theses:

  • Ana Crsitina Casimiro, "Propriedades geométricas e topológicas dos espaços de Brill-Noether de fibrados vectoriais sobre curvas algébricas", IST, 15/01/2001.
  • Sandra Bento, "Classificação de fibrados vectorias sobre superfícies de Riemann através de extensões," IST, 14/10/2002.
  • Lígia Carvalho, "Fibrados quase-parabólicos sobre a recta projectiva", IST, 4/3/2005. (Co-oriented by: Peter Gothen, Univ. Porto).
  • Susana Ferreira, "Semiestabilidade de fibrados vectoriais e principais sobre curvas elípticas", IST, 4/5/2007.
  • João Matias, "Classification of principal bundles over the Riemann sphere", IST, ULisboa, July, 2012.
  • Javier Alcaide, "Riemann surfaces and Dessins d'enfant", FC ULisboa, November, 2018.

Presentations (Slides):

Research Identifiers:

Ciência Vitae ID = 681B-1675-B20D
ORCID ID = 0000-0003-1001-0352
Google Scholar profile
Scopus Author ID = 6602533698
Researcher ID A-7883-2013

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