Federal University of Goias (UFG)
Research Productivity Fellow CNPq (C)
Adress: Instituto de Matemática e Estatística, Universidade Federal de Goiás, Campus Samambaia, CEP 74690-900, city: Goiânia, State of Goiás, Brasil, Room 211
Contact: luiz.goncalves@ufg.br
Welcome to my academic webpage!
I am an Assistant Professor (Professor Adjunto) at the Institute of Mathematics and Statistics (IME) of the Federal University of Goiás (UFG), Brazil, and a permanent faculty member of its Graduate Program in Mathematics. I currently serve as Research Coordinator of IME/UFG and hold a Research Productivity Fellowship from the National Council for Scientific and Technological Development (CNPq), Level C (PQ-C).
My research focuses on the qualitative theory of ordinary differential equations and dynamical systems, particularly piecewise smooth vector fields, limit cycles, bifurcation theory, geometric singular perturbation theory, and nonsmooth dynamical systems, with applications to physical and biological models.
I maintain active research collaborations with mathematicians from several Brazilian and international institutions, including USP, UNICAMP, UNESP, UNIFEI, and the Universitat Autònoma de Barcelona (UAB). I am also a member of the TeQA Network of Dynamical Systems, a Brazilian research network dedicated to the qualitative theory of dynamical systems and its applications.
My research has received support from CNPq, FAPEG, and FUNAPE through competitive funding programs, including research productivity fellowships, research grants, and scientific mobility support.
My research activities have been supported by the following fellowships, grants, and funding programs:
National Council for Scientific and Technological Development (CNPq) — Research Productivity Fellowship (PQ-C), Grant No. 303754/2026-5 (current).
Goiás State Research Support Foundation (FAPEG), in cooperation with the National Council for Scientific and Technological Development (CNPq) — Research Productivity Fellowship (PQ-C), awarded under CNPq Call No. 18/2024 through the FAPEG–CNPq Cooperation Agreement, Grant Process No. 202510267001611 (ended August 1, 2026).
National Council for Scientific and Technological Development (CNPq) — Universal Research Grant, Project No. 401974/2025-1, funded under Call CNPq/MCTI/FNDCT No. 44/2024.
Goiás State Research Support Foundation (FAPEG) — Research and scientific mobility support awarded under Calls No. 11/2024 and No. 21/2025.
Research Support Foundation (FUNAPE) — Research support awarded under Call No. 03/2024.
Federal University of Goiás (UFG) — Institutional Research Project PI05646-2021.
2020–2021 — Postdoctoral Research in Mathematics, University of São Paulo (USP), Brazil. Supervisor: Prof. Tiago de Carvalho.
2016–2020 — Ph.D. in Mathematics, São Paulo State University (UNESP/IBILCE), Brazil. Advisor: Prof. Tiago de Carvalho; Co-advisor: Prof. Luis Fernando Osório de Mello.
2014–2016 — M.Sc. in Mathematics, Federal University of Itajubá (UNIFEI), Brazil. Advisor: Prof. Luis Fernando Osório de Mello.
2010–2014 — B.Sc. in Mathematics, Federal University of Lavras (UFLA), Brazil.
My main research interests lie in the qualitative theory of differential equations and dynamical systems, with particular emphasis on:
Piecewise smooth and nonsmooth dynamical systems;
Limit cycles and bifurcation theory;
Geometric singular perturbation theory and regularization;
Sliding dynamics and Filippov systems;
Hamiltonian systems;
Minimal sets and chaotic dynamics;
Applications to biological and physical models.
USEFUL LINKS
TeQA Network of Dynamical Systems
The TeQA Network of Dynamical Systems is a Brazilian scientific initiative aimed at fostering collaboration among researchers and research groups working in the qualitative theory of dynamical systems and related fields, including their applications.
XIV Workshop on Dynamical Systems - OSD 2026
XIV Workshop on Dynamical Systems - OSD 2025
XIII Workshop on Dynamical Systems - MAT80
XII Workshop on Dynamical Systems
Dynamical Systems Seminar — UFG
A regular seminar organized by the Dynamical Systems Group at IME/UFG, bringing together graduate students and researchers working in dynamical systems and related areas.
Seminar on Topics in Dynamics
A research seminar organized by Prof. Rodrigo D. Euzébio and co-organized by Prof. Durval Tonon and Prof. Luiz Fernando Gonçalves.