Investigação

Interesses Científicos

Geometria Algébrica e Geometria Diferencial Complexa, Teoria dos Invariantes Geométricos, Variedades de Carácteres e Espaços de Moduli, Quantização Geométrica, Superfícies de Riemann, Física-Matemática

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Afiliação Científica

- CMAFcIO - Center for Mathematics, Fundamental Applications and Operations Research, Fac. Ciências, Univ. Lisboa (Coordenador actual)
- Colaborador em CAMGSD - Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Inst. Sup. Técnico, Lisboa e em GFMUL - Mathematical Physics Group of Univ. Lisbon, FCUL.

Projectos Internacionais

Tarefas Editoriais

Publicações

Artigos Científicos:

Character varieties:
  1. C. Florentino, Azizeh Nozad and Alfonso Zamora, "Generating series for the Hodge-Euler polynomials of GL(n,ℂ)-character varieties", Preprint arXiv:1902.06837.
  2. C. Florentino and J. Silva, "Hodge-Deligne polynomials of abelian character varieties", Preprint arxiv:1711.07909.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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).
  8. I. Biswas, C. Florentino, S. Lawton, M. Logares, "The Topology of Parabolic Character Varieties of Free Groups", Geom. Dedicata 168 (2014) 143-159.
  9. 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)
  10. C. Florentino and S. Lawton, "Singularities of free group character varieties", Pacific J. Math. 260 (2012) 149-179 (arxiv-math/0907.4720).
  11. C. Florentino and S. Lawton, "The topology of moduli spaces of free group representations", Math. Annalen 345 (2009) 453-489. (arxiv-math/0807.3317).
Moduli of bundles:
  1. A. Casimiro, S. Ferreira, C. Florentino, "Principal Schottky Bundles over Riemann surfaces". Preprint arxiv-math/1612.08662.
  2. I. Biswas and C. Florentino, "Higgs bundles and representation spaces associated to morphisms", Archivum Mathematicum 51 (2015), 191—199.
  3. I. Biswas, C. Florentino, L. Godinho, A. Mandini, "Symplectic form on hyperpolygon spaces", to appear in Geom. Dedicata.
  4. 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.
  5. I. Biswas and C. Florentino, "Commuting elements in reductive groups and Higgs bundles on abelian varieties", J. Algebra, 388 (2013) 194-202.
  6. 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.
  7. 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)
  8. 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.
  9. 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 (aqui em formato reduzido)).
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 e 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 e 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 e 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 e J. P. Nunes, "Coherent state transforms and Theta Functions", Proc. of Steklov Inst. of Math. 246 (2004) 283-302. (dedicado a A. N. Tyurin).
  7. C. Florentino, J. Mourão e 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 e 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.
Outros:
  • C. Florentino, "O número de pontos inteiros numa circunferência", Boletim da SPM 54 (2006).
  • L. Diogo, C. Florentino e D. Veloso, "Formas quadráticas e Fracções Contínuas", Escola Diagonal 2005.

Orientação (ou co-orientação) de teses de doutoramento

  • Susana Ferreira, "Schottky uniformization of principal bundles over Riemann surfaces", tese submetida em 2014 (co-orientação de Ana C. Casimiro (FCT, UNL)).
  • Jaime Silva, Bolseiro de pós-graduação FCT, Hodge-Deligne structures on character varieties. Conclusão prevista em 2017.

Orientação (ou co-orientação) de teses de mestrado

  • Ana Crsitina Casimiro, "Propriedades geométricas e topológicas dos espaços de Brill-Noether de fibrados vectoriais sobre curvas algébricas", 15/01/2001.
  • Sandra Bento, "Classificação de fibrados vectorias sobre superfícies de Riemann através de extensões," 14/10/2002.
  • Lígia Carvalho, "Fibrados quase-parabólicos sobre a recta projectiva", 4/3/2005. (Co-orientador Científico: Peter Gothen, Univ. Porto)
  • Susana Ferreira, "Semiestabilidade de fibrados vectoriais e principais sobre curvas elípticas", 4/5/2007.
  • João Matias, "Classification of principal bundles over the Riemann sphere", 7/7/2012. (pós-Bolohna).

Projectos Nacionais (já terminados)

Outros Projectos Passados

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