CV Lattes
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Universidade Federal de São Paulo (UNIFESP). Campus São José dos Campos. Instituto de Ciência e Tecnologia (ICT) (Institutional affiliation from the last research proposal) Birthplace: Brazil
graduation at Bacharelado Em Matemática from Instituto de Ciências Matemáticas e de Computação (2005), graduation at Licenciatura em Matemática from Instituto de Ciências Matemáticas e de Computação (2007), master's at Mestrado em Matemática from Instituto de Ciências Matemáticas e de Computação (2008) and doctorate at Mathematics from Universidade Estadual de Campinas (2012). Has experience in Mathematics, focusing on Algebra, acting on the following subjects: identidades polinomiais, polynomial identities, generic algebras, pi álgebras and álgebra. (Source: Lattes Curriculum)
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In this research project we want to study the form of the homogeneous automorphisms and involutions in graded matrix algebras and the relation between graded identities and weak equivalence of graded algebras. Also, we aim to study polynomial identities in relatively free algebras of finite rank of varieties of infinite basic rank. (AU)
This research project aims to study subvarieties of varieties of infinite basic rank and of small exponent in characteristic zero. More specifically, we intend to classify such subvarieties modulo asymptotic equivalence and study the identities of their relatively free algebras of finite rank. In another research topic, we aim to study the problem of determining the image of a noncommutat…
In this research project we aim to study images of polynomials on algebras with additional structures. More specifically, we will study images of polynomials on matrix algebras endowed with its usual Z-grading. We will try to prove results similar to those already known for the usual grading by the cyclic group of order n.We will focous on multilinear polynomials, trying to prove general …
This project aims to introduce the candidate to the theory of algebras with polynomial identities, more specifically to the problem of determining images of multilinear polynomial in certain associative and non-associative algebras.(AU)
This research project aims to introduce the student to the theory of nonassociative algebras, taking as main motivation algebraic structures arising from models of genetic inheritance.
The Lvov-Kaplansky conjecture states that the image of the matrix algebra $M_n(F)$, by a multilinear polynomial is a vector subspace of $M_n(F)$. There are many results in the literature, specially in the last 4 years, with partial answers for such problem and also for generalizations for some non-associative matrix algebras. The aim of this project is a detailed study of such results, a…
(Only some records are available in English at this moment)
The project will be dedicated to various aspects related to evaluation of polynomials in algebras. The goal is to continue the research already conducted by the proponent while also expanding their field of work by incorporating new aspects into the study of polynomial identities. Below, we highlight two main approaches in this project.One approach will focus on polynomial images in algeb…
The Lvov-Kaplansky conjecture states that the image of a multilinear polynomial on Mn(F) is a vector subspace of Mn(F). In this research project, we aim to study the image of multilinear polynomials on some classes of simple algebras. First we will consider images of graded polynomials on Mn(F) endowed with some types of elementary gradings and second we will consider images of polynomial…
In this research project, we aim to study the image of multilinear polynomials on some subalgebras of matrix algebras, such as the algebra of upper triangular matrices and other related problems.
| 1 / 1 | Ongoing grants |
| 3 / 3 | Completed research grants |
| 1 / 1 | Ongoing scholarships in Brazil |
| 6 / 5 | Completed scholarships in Brazil |
| 1 / 1 | Ongoing scholarships abroad |
| 2 / 2 | Completed scholarships abroad |
| 14 / 13 | All research grants and scholarships |
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