Herivelto Martins Borges Filho in research grants and scholarships supported by FAPESP.
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This project deals with algebraic curves over finite fields and their applications.The central theme underlying its development is the study of rational points in algebraic curves over finite fields. This includes obtaining new bounds for the number of rational points as well as characterizing curves reaching such bounds. This theme is transversal to several other relevant themes in the a…
This proposal establishes my research plans for the next two years or so. The core of the investigation are aspects the theory of curves over FiniteFields that are directly related to the number and nature of rational pointson such curves. (AU)
(Only some records are available in English at this moment)
This project has two main objectives: the first is to determine the number of rational points of Artin-Schreier hypersurfaces, which are hypersurfaces of the form y^q-y=f(X), with f(X) \in F_q[X]{0} and X=(x_1,...,x_r), imposing some conditions on f. This problem has already been partially studied in my Ph.D thesis in the case where f is a sum of binomials of the form a_j x_j(x_j^{q^{i_j}…
The main goals of this project are to understand better the conditions in which we are able to compute the number of elements in finite fields satisfying some suitable conditions and to obtain conditions that guarantee the existence of such elements. In general, the chosen problems are very interesting in the point of view of pure mathematics as well as for applications to Cryptography an…
The main focus of this project is the study of the theory of Finite Permutations Groups. Special emphasis will be given to the case of transitive permutation groups, from the basics to Frobenius and Mathieu Group. The long-term goal of the project is two-fold. On the one hand, the student shall learn the tools necessary to use permutation groups in current research problems; for instance,…
In this project, we will study properties of elliptic curves over Q, their associated Tate-Shafarevich groups and Selmer groups, with an eye towards a result by Bhargava-Skinner-Zhang (2014) which states that the majority (over 66 percent) of such elliptic curves, when ordered by height, satisfies the Birch and Swinnerton-Dyer conjecture, one of the main open problems in modern Number The…
(Only some records are available in English at this moment)
This document concerns an application for a BEPE-FAPESP postdoc scholarship at University of California, Irvine, under supervision of professor Daqing Wan from January 2019 till December 2019. As I have written in the research plan of the FAPESP postdoc, process 2017/21259-3, one of the main goals for the postdoc at ICMC-USP, is to expand my research area to the theory of rational poin…
This project aims to study the algebraic curves that correspond to the intermediate extensions on the Galois closure of the so-called multi-Frobenius non-classical curves and investigate its automorphism group. (AU)
We propose to investigate some questions related to the number of rational points on curves over finite fields. Most of these questions were raised after some recent work of the author regarding a variation of the Stohr-Voloch Theory. (AU)
| 1 / 1 | Ongoing research grants |
| 4 / 4 | Completed research grants |
| 1 / 1 | Ongoing scholarships in Brazil |
| 14 / 14 | Completed scholarships in Brazil |
| 3 / 3 | Completed scholarships abroad |
| 23 / 23 | All research grants and scholarships |
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