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Research

Please find below a list of the topics I have been working on. Should you be interested in any of them, please do not hesitate to contact me.

Main Lines of Research
Stochastic Rumors

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. 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, such as hypercubic lattices, (random) trees, small-world graphs, and so forth.

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Special Stochastic Processes and Random Structures

Keywords: percolation, random graph, branching process

Our research focuses on the study of special stochastic processes and random structures. In this context, our objective is to identify sufficient conditions that can be used to guarantee the existence of a phase transition. Among the models that we have considered, we have worked with inhomogeneous random graphs, the accessibility percolation model on (random) trees, and special branching processes with selection. Some of the processes that we have studied are also related to models of interacting random walks on graphs.

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Evolution Algebras

Keywords: genetic algebra, algebra isomorphism, derivation space

Evolution Algebras is a vibrant field of research with applications and connections to other mathematical subjects. In this line of research, we initiated our investigation by examining the properties of evolution algebras associated with graphs. On the one hand, we have established conditions under which certain isomorphisms of interest exist. On the other hand, we have provided a characterization of the space of derivations of such algebras. Currently, we are expanding our approaches to study general evolution algebras.

Stochastic Processes and Random Structures Research Group

The research group was established at CCEN/UFPE in 2019 by researchers and students with the objective of developing probabilistic and statistical methodologies for the study of complex systems. The group is certified by the Brazilian National Council for Scientific and Technological Development (CNPq).

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Collaborators

& Students

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. 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 Católica San Pablo (PER),  Universidad Nacional de la Patagonia - UNPSJB (ARG), Universidad de Nariño - UDENAR (COL) and Universidad de Antioquia - UDEA (COL).

Main co-authors

From Brazil

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)

Luz Marina Gomez (Federal Univ. of Pernambuco, UFPE)

Nancy Garcia (University of Campinas, UNICAMP)

Paula Cadavid (Federal Rural U. of Pernambuco, UFRPE)

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.

From abroad

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

Posdoc researcher

Mario Estrada (PPGE - Apr/2020 to Aug 2021, CAPES)

Carolina Grejo (PIPGEs - 2017 to 2019, CAPES)

 

Ph.D.

Jean Carlos Cardoso (PPGE - Nov/2023, FACEPE)

Adalto Speroto (PIPGEs - Apr/2021, CAPES)

Carlos Hirth (PIPGEs - Jan/2020, CAPES)

Karina Oliveira (PIPGEs - Apr/2019, CAPES/FAPESP)

 

Master

Débora Cordeiro (PPGE - Apr/2024, FACEPE)

Ana Diaz (PPGE - Abr/2024, FACEPE)

Jhon Puerres (PPGE - Aug/2023, CAPES)

João Gondim (PPGE - Jul/2023)

Luciano Mendes (PPGE - Aug/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

Posdoc researcher

Luz Marina Gomez (since Apr/2024, BFP-FACEPE)

Ph.D.

Jhon Puerres (PPGE - since Aug/2023, FACEPE)

Master

José Manuel Jaramillo (PPGE - since Mar/2023, FACEPE)

Maria Alves de França (PPGE - since Jan/2023, CAPES)

Christian Pistala** (UDENAR - COL - since Jul/2022)

Undergraduate

Mariana Caceres (Computer Science, U. Católica San Pablo - PER - since Mai/2024)*

*This project is (or was) part of the Scientific Mentoring Program from PPGE/UFPE. Mariana Caceres is co-advised with Daniel Pachas (UCSP - PER). Ana Diaz was co-advised with Catalina Rua (UdeNar - COL) and Jose Jaramillo was co-advised with Mary Luz Rodiño (UdeA - COL).  **Co-advising together with Catalina Rua (UdeNar - COL) in the Graduate Program in Applied Statistics from UdeNar (COL)

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