Carlos Henrique Grossi Ferreira

• Abstract

  The main goals of this research plan are the construction of new examples of complex hyperbolic disc bundles over closed orientable surfaces and the construction of new isometric embeddings between manifolds equipped with a classic geometry structure (as defined in [4] - see research plan). We expect to answer some relevant questions in complex hyperbolic geometry (see sections 3.2 and 4.…

  Classic geometries and the construction of hyperbolic manifolds, AP.R

• Abstract

  The main goal is to introduce the central aspects of Information Geometry and its major tools. At the same time, we expect to analyze these tools in the context of some classic geometries (hyperbolic, Fubini-Study, de Sitter, anti-de Sitter) and to explore the role of Information Geometry in such environment. Finally, we expect the applicant to understand some important applications of in…

  Information geometry and applications, BP.MS

• Abstract

  The main goal of the project is to introduce the normalized Ricci flow on compact surfaces. In particular, we expect the student to become acquainted with the technique of evolving metrics on smooth manifolds through partial differential equations and to appreciate the strength of such method (which is a central one in modern geometry). As a final result, the student should present a proo…

  An introduction to Ricci flow on surfaces, BP.IC

• Abstract

  The main goal of the project is to introduce Grothendieck's theory of schemes as an approach to algebraic geometry. The study of classical facts involving affine and projective varieties (as well as of the corresponding pre-requisites of commutative algebra) over algebraically closed fields will serve as a motivation to the necessity of introducing schemes when it comes, say, to algebraic…

  An introduction to schemes, BP.IC

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