My research focuses on the interaction between differential equations and their associated geometric and topological structures, emphasizing foliation theory and singularities. I am also interested in applications to mathematical physics and other interdisciplinary problems.

Recent preprints develop (i) the construction and classification of 2-flags of holomorphic foliations arising from singular second-order ODEs, and (ii) results on the topological invariance of algebraic multiplicity for broad classes of holomorphic foliations.

Motivated by mathematical physics, I have also studied non-perturbative phenomena (resurgence and transseries), and I am interested in interdisciplinary modeling, including resource-limited ecological dynamics via generalized Lotka–Volterra systems with memory effects.

Work in progress

(with Edson Sampaio) Topological Invariance of Algebraic Multiplicity of Holomorphic Foliations.
(with Jefferson Nogueira) Projective Connections and Invariant Hypersurfaces.
(with Herson Rocha and Josenilson Marinho) Tumor–Immune Dynamics and The Generalized Lotka–Volterra Model.

Published and accepted

(with Herson Rocha and Josenilson A. O. Marinho) HARMONIC TROPHIC POTENTIALS AND MEMORY EFFECTS IN ECOLOGICAL DYNAMICS IN RESOURCE-LIMITED ECOSYSTEMS THROUGH THE GENERALIZED LOTKA-VOLTERRA MODEL WITH BIOMASS CONSTRAINTS. Theory in Biosciences. (accepted for publication)
(N.M.Alvarenga, E.Cavalcanti, C.A.Linhares, J.A. Lourenço, J.R.P.Mahon) INSTATONS AND TRANSSERIES OF THE MATHIEU POTENTIAL DEFORMED BY A PT SYMMETRY PARAMETER. Brazillian Journal of Physics, 54:215, (2024). Link
(with Bruno Scardua (UFRJ)) ON THE INTEGRABILITY OF HILL'S EQUATION OF THE MOTION OF THE MOON. Journal of Mathematics and Statistics Research, v.5, 2, 2582, (2023). Link
(with Eurípedes da Silva(IFCE) and Maico Ribeiro(UFES)) TOPOLOGY OF FIRST INTEGRALS VIA MILNOR FIBRATIONS. Matematica comtemporanea, v.53, 2, 5-22, (2023). Link
(with Fernando Lourenço(UFLA)) A BRIEF INTRODUCTION ON RESIDUE THEORY OF HOLOMORPHIC FOLIATIONS. Matematica Contemporanea, v.53,2,181-212 (2023). Link
(with Eurípedes da Silva(IFCE) and David Souza (IFCE)) CHARACTERIZATION OF TOTALLY GEODESIC FOLIATIONS WITH INTEGRABLE AND PARALLELIZABLE NORMAL BUNDLE. Glasgow Mathematical Journal (2022).Link
(with Bruno Scardua) ON GERMS OF HOLOMORPHIC FOLIATIONS ADMITTING SECTORIAL FIRST INTEGRALS. Boletín de la Sociedad Matemática Mexicana (2021). Link
(with Maico Ribeiro (UFES) and Antonio do Espírito Santo (UFPB)) MILNOR-HAMM FIBRATION FOR MIXED MAPS. Bulletin Brazilian Mathematical Society (2020). Link
(with Maico Ribeiro (UFES)) UMA BREVE INTRODUÇÃO À TEORIA DAS CATEGORIAS. Revista Elementos (2012) Link

Submited

(with Fernando Lourenço(UFLA) and Euripedes da Silva (IFCE)); On flags of holomorphic foliations associated with singular second-order ordinary differential equations. https://arxiv.org/abs/2308.13370
(with Leonardo Camara(UFES) and Edson Sampaio(UFC)) On the topological invariance of the algebraic multiplicity of holomorphic foliations. https://arxiv.org/html/2407.09306

Chapter

Ribeiro, M. F. S. ; REIS, F. P. P. . Categorias. Teoria das Categorias para Matemáticos: uma breve introdução. 1ed.Rio de Janeiro: Editora da Sociedade Brasileira de Matemática, 2020, v. , p. 5-26.
Ribeiro, M. F. S. ; REIS, F. P. P. . Morfismos e objetos especiais. Teoria das Categorias para Matemáticos: uma breve introdução. 1ed.Rio de Janeiro: Editora da Sociedade Brasileira de Matemática, 2020, v. , p. 29-39.

Other publications

Master thesis 2011 (link: Soluções positivas de um sistema elíptico semilinear nos casos crítico e supercrítico )
Phd thesis 2019 (link: Methods from holomorphic foliations for second order ordinary differential equations)

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