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bachelor's at Bacharelado Em Matemática from Universidade Federal Fluminense (2002), master's at Mathematics from Universidade Federal Fluminense (2005) and doctorate at Mathématiques Pures from Institut de Mathématiques de Toulouse (2009). Has experience in Mathematics, focusing on Defferential Geometry, acting on the following subjects: seifert manifolds, geometric structures, hyperbolic cone-manifolds, fibration theorem and metric geometry. (Source: Lattes Curriculum)

Research grants

- Weingarten surfaces in R^3 and complete hypersurfaces with negative Ricci curvature in R^{n+1}, AV.BR
### Abstract

This research project is divided into two parts. In the first one we are interested in studying Weingarten surfaces, that is, surfaces in which there is a (possibly nonlinear) relationship between their principal curvatures. Almost all works in the literature deal with the linear case, however the techniques used in them do not apply to the nonlinear case. We will seek in our investigat...

- Weingarten Surfaces, Self-Shrinkers and hyperbolic surfaces, AP.R
### Abstract

This research project concerns Riemannian surfaces and it is divided into three parts..In the first part of the project we are interested in studying Weingarten surfaces, that is, surfaces whose principal curvatures verify a certain relation (generally polynomial) over the entire surface. In the second part of the project we are interested in studying self-shrinkers surfaces that appear...

- Geometric manifolds and Orbifolds of dimension 3, AP.R
### Abstract

In this project we want to develop a study about geometric manifolds and orbifolds of dimension 3. That is, manifolds and orbifolds obtained from the quotient of the eight model geometries of Thurston by discrete groups of isometries. Special attention will be given to Sol and hyperbolic classes.In the first part of the project, we are interested in classifying the double coverings and ...

Scholarships in Brazil

- Weingarten surfaces, BP.IC
### Abstract

A Weingarten surface S in a three-dimensional Riemannian (or semi-Riemannian) manifold is a regular surface whose principal curvatures k1 and k2 verify a relationship (usually polynomial, but not necessarily) P (k1, k2) = 0. Since the mean and Gaussian curvatures H and K determine/are determined by the principal curvatures of S, the relation P can always be rewritten in the form Q (H, K...

- Introduction to hyperbolic geometry, BP.IC
### Abstract

The main purpose of this scientific initiation project is to develop the mathematical maturity of the student and to stimulate his curiosity and his scientific interest. The theme chosen to achieve this purpose was Hyperbolic Geometry because it allows an interesting interconnection between General Topology concepts and Differential Geometry (studied by the student in the last year, in ...

- Introduction to algebraic topology, BP.IC
### Abstract

The current scientific initiation project has as main goals to develop the student mathematical maturity and scientific interest. The chosen theme to reach this purpose was Algebraic Topology, more precisely Homology Theory, whose importance in Mathematica is notorious. Besides being a well-sophisticated research area, the prerequisite needed for the proposed study was acquired by the s...

- Minimal surfaces and the Almgren-Pitts Min-Max theory, BP.MS
### Abstract

Since the works of Schoen and Yau in the late 70's, it became clear that the existence of a minimizing area surface might to exert great influence on the geometry of a Riemannian 3-manifold. Along the last few years, researchers as M.Cai, G.J.Galloway, H.Bray, S.Brendle, F.C.Marques and A.Neves have proved several rigidity results which made use of the existence of such minimizing sur...

- The Thurston earthquakes theorem on Teichmüller spaces, BP.MS
### Abstract

The study of 2-dimensionals and 3-dimensionals manifolds begins with Henry Poincaré in the late 19th century. At the beginning of the 20th century, Poincaré conjectured that any tridimensional closed manifold with trivial homology should be homeomorphic to a sphere. This famous conjecture, as known as "Poincaré Conjecture", conducted the researches in low-dimensional topology (dimension...

- Introduction to general topology, BP.IC
### Abstract

The General Topology has as its central object of study the continuous functions between topological spaces. Unlike what was seen by the student in the courses of Differential Calculus, the notion of continuous function in this context makes absolutely set-theoretic, in other words, without a metric involved. This paradigm shift is extremely aggrandizing for the beginner mathematician s...

(Only some records are available in English at this moment)

Scholarships abroad

- Min-Max minimal surfaces, BE.EP.MS
### Abstract

We will study the Almgren--Pitts Min-Max method to construct and analyze minimal surfaces. Our research will be guided by the recent article Rigidity of min-max minimal spheres in three-manifolds, by F. C. Marques and A. Neves, where it is proved, among other results, that any metric on a three-sphere which has scalar curvature greater than or equal to 6 and is not round must have an em...

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| Ongoing scholarships in Brazil |

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| Completed scholarships in Brazil |

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| Completed scholarships abroad |

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| All research grants and scholarships |

Associated processes |

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

Publications | 2 |

Citations | 0 |

Cit./Article | 0.0 |

Data from Web of Science |

BARRETO, ALEXANDRE PAIVA. On the collapsing along deformations of hyperbolic cone 3-manifolds.** KYOTO JOURNAL OF MATHEMATICS**, v. 56, n. 3, p. 539-557, SEP 2016. Web of Science Citations: 0. (14/23398-2)

BARRETO, ALEXANDRE PAIVA. DEFORMATION OF THREE-DIMENSIONAL HYPERBOLIC CONE STRUCTURES: THE NONCOLLAPSING CASE.** PACIFIC JOURNAL OF MATHEMATICS**, v. 268, n. 1, p. 1-21, MAR 2014. Web of Science Citations: 0. (09/16234-5)

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