CV Lattes
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Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC) (Institutional affiliation from the last research proposal) Birthplace: Brazil
Associate professor (MS-5.3 level, since 2021) at the Department of Mathematics, ICMC-USP, São Carlos, conducting research in the field of Singularities/Dynamical Systems, with an emphasis on the study of singularities of vector fields, focusing primarily on topics related to polynomial vector fields, bifurcation theory, Darbouxian integrability, polynomial invariants, center-focus problem, and piecewise continuous differential systems. Recipient of CNPq Research Productivity Grant, level 1D (since March 2020), principal investigator of a FAPESP Thematic Project, and advisor for the postgraduate programs in Mathematics at ICMC-USP and PROFMAT-ICMC-USP. Holds a bachelor's degree in Mathematics from IGCE-UNESP, Rio Claro (1995), a Ph.D. in Mathematics from ICMC-USP, São Carlos (2000), and completed postdoctoral research at IMECC-UNICAMP (2003) and Universitat Autònoma de Barcelona, Spain (2007). (Source: Lattes Curriculum)
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Singularity theory has wide applications to several areas of science such as optics, robotic and computer vision, and interacts with several areas of mathematics, among which we highlight the algebraic geometry and algebraic topology, commutative algebra, differential and affine geometry, the qualitative theory of ordinary differential equations, dynamical systems, and bifurcation theory.…
The main focus of this project is related with the existence of first integrals (A non constant and smooth functions a real values defined on open set $U$ of a manifold that is constant on the solution of the system). Using the knowlegde of distinct tools and diferent approaches we hope to contribute with the investigation on the global behavior of polynomial differential systens defined …
This project belongs to the study of quadratic differential systems on the plane. There are more than one thousand papers published in quadratic polynomial differential systems (or simply quadratic systems). The difficulty of studying these differential systems is due to the fact that they depend on twelve parameters. Nowadays there are still many open questions regarding quadratic system…
(Only some records are available in English at this moment)
In this research project, we propose to study the results presented by Brunella and Miari in the article entitled Topological equivalence of a plane vector field with its principal part defined through Newton Polyhedra, as well as the tools necessary to obtain such results. In particular, we aim to explore the strong relationship between fields of non-degenerate vectors and toric varietie…
This project aims to introduce the candidate to some significant outcomes of the Qualitative Theory of Ordinary Differential Equations (ODEs) and their applications. Among the results to be studied, we highlight the Theorems of Tubular Flow, Poincaré-Bendixson, and the Integrability Theory for systems defined in the plane.It is worth noting that the student has already explored crucial to…
This project deals with the periodic function of centers. A critical point p of a planar differential system is called a center if it has a neighborhood consisting entirely of periodic orbits. The largest neighborhood with this property is called the annular period of the center. The period function of the center assigns a period to each periodic orbit in the annular period. If the period…
(Only some records are available in English at this moment)
The objective of this project is to introduce a undergraduate student in Mathematics to the central problem and the cyclicity problem for planar polynomial differential systems. The main idea is that the student has the first contact with the basic tools and results of the subject, as to introduce her to the computational tools available for this kind of investigation.(AU)
Differential equations have a remarkable in the description of phenomena around the world and specially to understand phenomena that involve rates. Some of these equations can be solved using differential calculus methods, but most of them require more sophisticated tools. Furthermore, differential equations can be found, for instance, in Medicine (to model the growth of cancer or the spr…
In this project we shall study qualitatively ordinary differential equations, emphasizing the study of singular points, phase portraits, bifurcations and applications to several areas. (AU)
(Only some records are available in English at this moment)
The Sotomayor-Teixeira regularization is widely used in the study of theoretical and applied aspects of piecewise smooth vector fields. In addition, the study of different regularization processes, such as non-monotonic and non-linear regularizations, has attracted attention because it expands the possibilities of the dynamics of the associated slow-fast system. This research project aims…
This project aims to introduce the different concepts of centers in planar differential systems, and their characterizations via the integral first of their corresponding systems.
The integrability problem consists of explicitly finding a non-constant function that is constant on the orbits of a given system. For planar differential systems, the integrability theorypar excellence is Darboux's. Generalizations of this theory have been achieved during thelast few years, such as the integrability based on generalized cofactors and the Weierstrassintegrability, for exa…
(Only some records are available in English at this moment)
| 1 / 1 | Ongoing grants |
| 10 / 10 | Completed research grants |
| 7 / 7 | Ongoing scholarships in Brazil |
| 14 / 9 | Completed scholarships in Brazil |
| 6 / 6 | Completed scholarships abroad |
| 38 / 33 | All research grants and scholarships |
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