Here you can find some information about me, my research, and those courses that I have taught or currently teaching.
I am an Adjunct Professor in the Department of Statistics at the Federal University of Pernambuco (UFPE), located in the city of Recife, PE, Brazil. Also I am the President of the Brazilian Society for Applied and Computational Mathematics (SBMAC). My current research activity can be divided into three broad lines. The main part is focused in using interacting particle systems, percolation models and special stochastic processes on graphs to describe the spread of an information and other similar phenomena on a population. More precisely, I work with stochastic rumors! Also, I am interested in studying (asymptotical) properties of random structures inspired by biological questions, and related subjects of discrete mathematics. This includes some percolation and random graph models. Finally, and more recently, I started to get involved in studying a new algebraic structure called evolution algebra. My interest in this subject is because it has been suggested in the literature the existence of a nice interplay between this concept and some notions related to discrete-time Markov chains.
Photo: Elã Café, Recife, 2022.
Keywords: epidemic-like model, Markov chain, information transmission.
We propose and study stochastic models describing in a simple way the phenomenon of information transmission on a population. We consider modified versions of the Maki-Thompson rumor models, but also we study related models like the Bass model for innovation diffusion. Our results are related to the existence of phase transition and the asymptotic behavior of such processes on homogeneously mixing populations or population represented by different graphs like hypercubic lattices, (random) trees, small-world graphs etc.
Keywords: percolation, random graph, branching process.
We study special stochastic processes and random structures. In this direction, our interest is the statement of sufficient conditions under which we can guarantee the existence of a phase transition. Between the considered models we have worked with an inhomogeneous random graph; with the accessibility percolation model on (random) trees; and with special branching processes with selection.
Keywords: genetic algebra, algebra isomorphism, derivation space.
The Theory of Evolution Algebras is an active field of research with applications and connections with other mathematical subjects. In this line of research we are studying the properties of evolution algebras associated to graphs. On the one hand we have stated conditions under which some isomorphisms of interest exist. On the other hand, we provide a characterization of the space of derivations of such algebras. Currently, we are extending our approaches to study general evolution algebras.
My Erdös number is 3
(I haved worked with Kang who worked with Loebl who worked with Erdös).
My Mathematics Genealogy is given by
Fabio Machado (and Elcio Lebensztayn), Pablo Ferrari, Enrique Andjel, Thomas Liggett, Karlin, Bochner, Schmidt, Hilbert, Lindemann, Klein, Plücker, Gerling, Gauss, Pfaff, Kästner, Hausen, Witchmannshausen, Mencke, Thomasius, and Leibniz (1643)!
Here is the list of those courses that I have taught or currently teaching. As they have been taught in Brazil, and since this information is mostly to my current students, I present the list in Portuguese!
Pós-graduação em Estatística da UFPE (desde 2019)
PGE950 - Probabilidade
PGE952 - Seminários de Pós-graduação
PGE966 - Processos Estocásticos
PGE998 - Probabilidade Avançada I
Pós-graduação em Estatística USP/UFSCar (2013-2018)
EST5101 - Teoria das Probabilidades
EST5525 - Processos Estocásticos
EST5531 - Modelos Probabilísticos
EST5805 - Tópicos Avançados de Pesquisa II
EST5801 - Probabilidade Avançada
Disciplinas de graduação na UFPE (desde 2019)
ET581 - Probabilidade 1 (Estatística)
ET582 - Probabilidade 2 (Estatística)
ET584 - Probabilidade 4 (Estatística)
ET658 - Processos Estocásticos (Ciências Atuariais)
ET199 - Estatística e Probabilidade (Matemática)
Disciplinas de graduação na USP (2012-2018)
SME0800 - Probabilidade I (Estatística)
SME0801 - Probabilidade II (Estatística)
SME0805 - Processos Estocásticos (Estatística)
SME0872 - Demografia (Estatística)
SME0120 - Int. à teoria de probabilidade (Computação)
SME0121 - Processos Estocásticos (Computação)
Depatamento de Estatística, Centro de Ciências Exatas e da Natureza (CCEN), Universidade Federal de Pernambuco (UFPE)
Av. Jornalista Aníbal Fernandes, 497-629 - Cidade Universitária, Recife - PE, 50740-540