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
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
- Vector bundles on algebraic curves, Annual European Conference (membro do Comité Científico)
- GEAR - Geometric Structures and Representation Varieties, NSF, USA (IR do nó de Lisboa)
Tarefas Editoriais
- Editor do Boletim do CIM - Centro Internacional de Matemática
- Editor do Boletim da Sociedade Portuguesa de Matemática.
Publicações
Artigos Científicos:
Character varieties:
- C. Florentino, Azizeh Nozad and Alfonso Zamora, "Generating series for the Hodge-Euler polynomials of GL(n,ℂ)-character varieties", Preprint arXiv:1902.06837.
- C. Florentino and J. Silva, "Hodge-Deligne polynomials of abelian character varieties", Preprint arxiv:1711.07909.
- 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.
- 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.
- 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.
- 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.
- 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).
- I. Biswas, C. Florentino, S. Lawton, M. Logares, "The Topology of Parabolic Character Varieties of Free Groups", Geom. Dedicata 168 (2014) 143-159.
- 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)
- C. Florentino and S. Lawton, "Singularities of free group character varieties", Pacific J. Math. 260 (2012) 149-179 (arxiv-math/0907.4720).
- 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:
- A. Casimiro, S. Ferreira, C. Florentino, "Principal Schottky Bundles over Riemann surfaces". Preprint arxiv-math/1612.08662.
- I. Biswas and C. Florentino, "Higgs bundles and representation spaces associated to morphisms", Archivum Mathematicum 51 (2015), 191—199.
- I. Biswas, C. Florentino, L. Godinho, A. Mandini, "Symplectic form on hyperpolygon spaces", to appear in Geom. Dedicata.
- 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.
- I. Biswas and C. Florentino, "Commuting elements in reductive groups and Higgs bundles on abelian varieties", J. Algebra, 388 (2013) 194-202.
- 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.
- 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)
- 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.
- 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:
- 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).
- 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).
- 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.
- 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.
- 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)
- 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).
- 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)
- 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:
- 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)
- 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).
- 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)
- (Ir)regular singularities and Quantum Field Theory, Co-Principal Investigator, FCT Project QuantumG PTDC/MAT-PUR/30234/2017
- Fibrados de Higgs e Variedades de Carácteres, FCT project PTDC/MAT/120411/2010 (Investigador Responsável)
- Geometry and Mathematical Physics, FCT Project EXCL/MAT-GEO/0222/2012
- GA-P - Geometria Algébrica em Portugal, FCT, PTDC/MAT-GEO/0675/2012 ("Core CV" member)
- Geometria da Quantização, FCT, PTDC/MAT/119689/2010 , 2012—2014