See here some particular topics I have been working on, and feel free to contact me if you are interested in some of them!
Main Lines of Research
Keywords: epidemic-like model, Markov chain, information transmission.
We propose and study stochastic models inspired by the phenomenon of information spreading in a population. Some of our models may be seen as modified versions of the Daley-Kendall or Maki-Thompson rumor models, and our results are related to the existence of phase transition and the asymptotic behavior of such processes. We consider both homogeneously mixing populations or populations represented by different graphs like hypercubic lattices, (random) trees, small-world graphs etc.
Special Stochastic Processes and Random Structures
Keywords: percolation, random graph, branching process.
We study special stochastic processes and random structures. In this direction, our interest is the obtention of sufficient conditions under which we can guarantee the existence of a phase transition. Between the considered models we have worked with inhomogeneous random graphs; the accessibility percolation model on (random) trees; and with special branching processes with selection. Some of the studied processes are also related to models of interacting random walks on graphs.
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 started by 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.
Stochastic Processes and Random Structures Research Group
The research group was created at CCEN/UFPE in 2019 by researchers and students with the aim of developing Probabilistic and Statistical methods for the study of Complex Systems. The Group is certified by the Brazilian National Council for Scientific and Technological Development (CNPq).
I have supervised students in the following Graduate Programs. PPGE: Graduate Program in Statistics - UFPE. CCMC: Graduate Program in Computer Science and Computational Mathematics. PIPGEs: Joint Graduate Program in Statistics UFSCar/USP. DCI: Ph.D. Program in Engineering Sciences at the UNPSJB - Argentina. PROFMAT: Professionalizing Master's Program in Mathematics ICMC-USP/SBM. In addition, I have supervised undergraduate students from ICMC/USP, and I have co-supervised undergraduate students from Universidad Nacional de la Patagonia - UNPSJB (ARG), Universidad de Nariño - UDENAR (COL) and Universidad de Antioquia - UDEA (COL).
Alex Ramos (Federal University of Pernambuco, UFPE)
Alejandra Rada (Federal University of ABC, UFABC)
Caliteia Sousa (Federal University of Pernambuco, UFPE)
Carolina Grejo (Center for Learning and Mobilization for Citizenship, CAMPC)
Cristian Coletti (Federal University of ABC, UFABC)
Elcio Lebensztayn (University of Campinas, UNICAMP)
Fabio Machado (IME-University of São Paulo)
Francisco Rodrigues (ICMC-University of São Paulo)
Nancy Garcia (University of Campinas, UNICAMP)
Paula Cadavid (Federal University of ABC, UFABC)
Renato Gava (Federal University of São Carlos, UFSCar)
Sandro Gallo (Federal University of São Carlos, UFSCar)
Valdivino Vargas (Federal University of Goiás, UFG)
I also published papers with my former students Adalto Speroto, Carlos Hirth, Karina E. de Oliveira, Matheus Souza, Thomas Freud.
Alejandro Roldán (Universidad de Antioquia, COL)
Alexander Valencia (Universidad de Antioquia, COL)
Angelica Pachon (University of South Wales, UK)
Catalina Rua (Universidad de Nariño, COL)
Daniela Bertacchi (Università Milano-Bicocca, ITA)
Elena Agliari (Sapienza Università di Roma, ITA)
Fabio Zucca (Politecnico di Milano, ITA)
Mario Estrada (Univ. Nacional Colombia, COL)
Mary Luz Rodiño (Universidad de Antioquia, COL)
Nevena Maric (Union University, SER)
Guilherme Ferraz de Arruda (CENTAI, ITA)
Mihyun Kang (Graz University of Technology, AUS)
Rinaldo Schinazi (University of Colorado, USA)
Sebastián Vidal (Universidad Nac. de la Patagonia, ARG)
Yamir Moreno (Universidad de Zaragoza, SPA)
Yolanda Cabrera Casado (Universidad de Málaga, SPA)
Posdocs and Students
Posdoc Supervised and Former Students
Mario Estrada (PPGE - Apr/2020 to Aug 2021, CAPES)
Carolina Grejo (PIPGEs - 2017 to 2019, CAPES)
Adalto Speroto (PIPGEs - Apr/2021, CAPES)
Carlos Hirth (PIPGEs - Jan/2020, CAPES)
Karina Oliveira (PIPGEs - Apr/2019, CAPES/FAPESP)
Luciano Mendes (PPGE - Ago/2022, FACEPE)
Diego da Silva Santos (PPGE - Fev/2022, CAPES)
Thomas Freud (PPGE - Fev/2022, CAPES)
Ricardo Caldas (PIPGEs - Fev/2020)
Dimas Rocha (PROFMAT - Fev/2018, CAPES)
Elizbeth Bedia (PIPGEs - Mar/2016, CAPES)
Eduardo Sartoretto (CCMC - Mar/2016, CNPq)
Cristel Vera Tapia (PIPGEs - Mar/2015, CAPES)
Karina E. de Oliveira (CCMC - Jan/2015, FAPESP)
Undergraduate Projects (TCC)
Jose Jaramillo (Maths, U. Antioquia - COL - Abr/2022)**
Ana Diaz (Mathematics, U. de Nariño - COL - Fev/2022)*
Matheus Souza (Statistics, USP - Ago/2019, CNPq)
Caio Moura (Statistics, USP - Jul/2017, FAPESP)
Emanuel Rodriguez (Informatics, UNPSJB - ARG - Sep/16)
Current Posdoc and Students
Jean Carlos Cardoso (PPGE - since Apr/2020, FACEPE)
Nelson Villagra (DCI - since Mar/2018, UNPSJB)
José Manuel Jaramillo (PPGE - since Mar/2023, FACEPE)
Maria Alves de França (PPGE - since Jan/2023, CAPES)
Christian Pistala*** (UDENAR - COL - since Jul/2022)
Jhon Puerres (PPGE - since Jun/2022, CAPES)
Ana Diaz (PPGE - since Fev/2022, FACEPE)
João Gondim (PPGE - since Fev/2022)
Débora Cordeiro (PPGE - since Mai/2021, FACEPE)
*Co-advised together with Catalina Rua (UdeNar - COL). This project was part of the Scientific Mentoring Program from PPGE/UFPE.
**Co-advised together with Mary Luz Rodiño (UdeA - COL). This project is part of the Scientific Mentoring Program from PPGE/UFPE.
***Co-advising together with Catalina Rua (UdeNar - COL) in the Graduate Program in Applied Statistics from UdeNar (COL)