Research
Scientific Interests
Complex Algebraic and Differential Geometry, Moduli Spaces and Character Varieties, Geometric Invariant Theory, Riemann Surfaces, Mathematical-Physics
Research Center
Research Project as Principal Investigator
- Higgs Bundles and Character Varieties, FCT project PTDC/MAT/120411/2010 , 2012—2014
Other current Research Projects
- Geometry of Quantization, FCT, PTDC/MAT/119689/2010 , 2012—2014
- GA-P - Geometria Algébrica em Portugal, FCT, PTDC/MAT/099275/2008 , 2010-2012
- Vector bundles on algebraic curves, Annual European Conference
Publications
Scientific Articles:
- I. Biswas, C. Florentino, J. Mourão, J. P. Nunes, "Quantization of some moduli spaces of parabolic vector bundles on CP^1", Preprint arXiv:1111.4838
- C. Florentino and S. Lawton, "Character Varieties and the Moduli of Quiver Representations", Preprint arXiv:1104.2960
- C. Florentino and T. Ludsteck, "Unipotent Schottky bundles on Riemann surfaces and complex tori", Preprint arxiv:1102.3006
- C. Florentino and S. Lawton, "Singularities of free group character varieties", Preprint arxiv-math/0907.4720.
- A. C. Casimiro and C. Florentino, "Stability of Affine G-varieties and Irreducibility in Reductive Groups", To appear in Int. J. Math. Preprint arXiv:1110.4236
- 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)
- 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 and S. Lawton, "The topology of moduli spaces of free group representations", Math. Annalen 345 (2009) 453-489. arxiv-math/0807.3317.
- C. Florentino, "Simultaneous similarity and triangularization of sets of 2 by 2 matrices", Lin. Alg. and Applications 431 (2009) 1652-1674.
- C. Florentino, "Invariants of 2 by 2 matrices, irreducible SL(2,C) characters and the Magnus trace map", Geom. Dedicata 121 (2006) 167-186.
- 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, Contemp. Math. 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.
- 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)).
Other Articles:
- 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.
Supervision of PhD Theses
- Susana Ferreira, "Schottky uniformization of principal bundles over Riemann surfaces" (co-orientation by Ana C. Casimiro. expected finishing year - 2012).
Supervision of Master Theses
- 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-oriented by: Peter Gothen, Univ. Porto).
- Susana Ferreira, "Semiestabilidade de fibrados vectoriais e principais sobre curvas elípticas", 4/5/2007.
