Welcome

Here you can find some information about me, my research, and those courses that I have taught or currently teaching.

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About me

I am an Assistant 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.

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Photo: UNS - ARG, 2019.

Research

See some particular topics I have been working on, and feel free to contact me if you are interested in some of them!

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Stochastic Rumors

Keywords: epidemic-like model, Markov chain.

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 Daley-Kendall and the Maki-Thompson rumor models, but also we study related models like the Bass model for innovation diffusion. Our results are related to the asymptotic behavior of such processes on homogeneously mixing populations or population represented by some regular graphs like hypercubic lattices and trees.

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Evolution Algebras

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.

Figure adapted from Kang et al. (2018)

Random Structures

Keywords: percolation, random graph, branching process.

We study percolation and random graph models. 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 the frog model on trees. The later is a system of interacting random walks which can be interpreted as a long range percolation model on infinite graphs.

Mathematical Curiosities:

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)!

Academic Profiles:

                                                    

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Teaching

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

Pós-graduação em Estatística da UFPE (desde 2019)

PGE950 - Probabilidade

PGE952 - Seminários de Pós-graduação

PGE966 - Processos Estocásticos  

PGE977 - Tópicos Especiais em 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

Graduação

Disciplinas de graduação na UFPE (desde 2019)

ET581 - Probabilidade 1 (Estatística)

ET582 - Probabilidade 2 (Estatística)

ET584 - Probabilidade 4 (Estatística)

ET658 - Processos Estocásticos (Ciências Atuariais) - 2021.1

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)

 

Contact

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