André Salles de Carvalho in research grants and scholarships supported by FAPESP.
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The present pre-project continues the work of three previous Thematic Projects supported by FAPESP with numbers 2006/03829-2, 2011/16265-8, and 2016/25053-8. The research group includes established researchers working in dynamical systems and low-dimensional geometry. Younger researchers will be included later in the full project as associated researchers. The areas covered by the project…
This project is a continuation of two previous thematic projects supported by FAPESP with numbers 2006/03829-2 and 2011/16265-8. The present group includes researchers working on dynamical systems and low-dimensional geometry and has senior as well as and young researchers, including recent hires. The areas covered by the project are: dynamics in dimension 2: dynamics of homeomorphisms an…
We plan to study limits of dynamical systems from different, but closely related, points of view: holomorphic dybamics in one variable, Kleinian and Fuchsian groups and dynamics of surface homeomorphisms. These subjects are closely related to 3-dimensional hyperbolic geometry and to explore this relationship is also an important part of the project. (AU)
(Only some records are available in English at this moment)
This project studies random compositions of homeomorphisms of surfaces, particularly of homeomorphisms of $\T^2$ in the isotopy class of the identity. While the usual techniques for assessing complexity of dynamical behaviour of cocycles of diffeomorphisms is the study of Lyapunov exponents, we intend to apply Brouwer theory and rotation theory like techniques in our study. Our main goa…
This project aims to investigate the interplay between the following three areas of study: Teichmüller theory, dynamical systems, and real/complex hyperbolic geometry. Traditionally, Teichmüller's theory is based on complex analysis and hyperbolic geometry. One of the objectives of this project is to investigate Teichmuller theory from the viewpoint of classic geometry (an approach to hy…
This project proposes to study the relationship between complex dynamics and 3-manifolds. A recent construction due to Carvalho-Meyer associates to an expanding Thurston map of the 2-sphere a singular 3-manifold with additional structures such as a pair of singular foliations and a singular-Euclidean metric. The project proposes to describe the topological characteristics of the 3-manifo…
The importance of manifolds with constant sectional curvatures equal to -1 can hardly be overstated. Some of the milestones in modern Mathematics, such as Riemann's Uniformisation Theorem and Thurston's Hyperbolisation Theorem, revolve around hyperbolic 2- and 3-manifolds. These objects, in turn, are inexorably linked to the understanding of Fuchsian and Kleinian groups.The arithmetic pro…
The objective of the project is the study of the topology and geometry of low-dimensional manifolds, with emphasis on 3-manifolds, and will be based, mainly, but not exclusively, on the notes "Topology and geometry of 3-manifolds: a pleasant introduction" (in Portuguese) written by the advisor of the project in collaboration with Rafael Siejakowski, of IME-USP, for an introductory course …
The project aims to study the topology and geometry of 3-manifolds, and is based on the notes ``Topology and Geometry of 3-manifolds: A Pleasant Introduction'', prepared by the advisor of this project in collaboration with Rafa B Siejakowski, from IME-USP, to accompany an introductory course of the same title at the 33rd. Brazilian Mathematics Colloquium. Topics to be discussed include in…
(Only some records are available in English at this moment)
The focus of my research is to study arithmetic properties of Fuchsian groups in order to better understand geometric invariants of their associated hyperbolic surfaces. This project is built around the question of determining the commensurability class of a Fuchsian group from its length spectrum. More precisely, we aim to apply the techniques developed in the work of A. Reid to a broade…
In [BdCH21], a continuous family of sphere homeomorphisms was constructed which is a mild quotient of the inverse limit of the tent family of interval endomorphisms. This family has the unimodal generalized pseudo-Anosov (ugpA) maps as a countable, dense subfamily, whose spheres of definition have well defined (and much studied) geometric structures. The purpose of the project is to prove…
The aim of this proposal is to study dynamics in dimensions 1 and 2 and its connections with geometric structures in dimensions 2 and 3. There are two starting points for the proposed research: first, the existence of ``good'' dynamical models for surface diffeomorphisms and families of such diffeomorphisms and, second, the relationship between 1- and 2-dimensional dynamics with interest…
| 1 / 1 | Ongoing grants |
| 8 / 7 | Completed research grants |
| 3 / 3 | Ongoing scholarships in Brazil |
| 20 / 17 | Completed scholarships in Brazil |
| 1 / 1 | Ongoing scholarships abroad |
| 2 / 2 | Completed scholarships abroad |
| 35 / 31 | All research grants and scholarships |
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