Personal Biography: Born in the historic and vibrant Caribbean city of Cartagena, Colombia.
Educational Background: My academic career began at the University of Cartagena, in the city where I was born, and continued at the Institute of Pure and Applied Mathematics (IMPA) in Brazil, where I obtained my Master's degree in 2009 and my PhD in 2013 in the field of dynamical systems and ergodic theory.
Work Experience: My professional career began in 2013 as a postdoctoral researcher at the Institute of Pure and Applied Mathematics (IMPA) with a Palis-Balzan Fellowship. From 2014 to 2020, I was a tenured assistant professor at the Federal University of Rio de Janeiro (Brazil), and from 2021 to 2024, I served as an Associate Professor at the same University. During this period, I collaborated with various research groups worldwide. Recently, from August 2023 to August 2024, I worked as a Visiting Fellow at SUSTECH (Shenzhen), fostering collaboration between China and Brazil. I have also served as an advisor to 2 undergraduate students, 4 Master's students, and 4 PhD students. Since January 2025, I have embarked on a new journey as an Associate Professor in the School of Mathematics (Zhuhai) at Sun Yat-Sen University.
Research Areas: My research expertise lies in dynamical systems and ergodic theory, with an interplay between differential geometry and number theory. The main focus is on combining tools from these areas to identify natural invariants that appear more intuitive from the perspective of the other field.
Research Projects: Throughout my scientific career, I have participated in various academic projects, including research and mathematics development projects. The research projects primarily focus on advancing rigidity problems using dynamical and ergodic techniques. The development projects aim to implement the fascination of mathematics, from basic education to university, with an emphasis on disseminating and applying mathematical knowledge.
Awards and Recognitions: My research has been widely recognized. In 2017, I was invited to give a lecture at the Mathematics Congress of the Americas (MCA) in Montreal. In 2019 and 2023, I received grants from the Internationalization of Universities Program (prInt) by the Brazilian government to visit Nankai University (Tianjing), Sustech (Shenzhen), and City University of New York (CUNY). In 2022, I was awarded the "Young Researcher of the State of Rio de Janeiro" grant by the Research Support Foundation of the State of Rio de Janeiro (FAPERJ), a recognition of my contribution to the development of mathematical science in Brazil.
Thoughts on Joining the Team: Joining the School of Mathematics (Zhuhai) at Sun Yat-Sen University has been the most exciting moment of my academic and personal life. The kindness, dedication, and enthusiasm of all members of the School of Mathematics (Zhuhai) make me feel at home. Furthermore, the interdisciplinarity and expertise of my colleagues create an environment of complete development, and I am eager to be part of this growth, overcome new challenges, and actively contribute to the advancement of our School of Mathematics (Zhuhai).
Students
Phd Students
1.Davi Lima (Coadvisor - Graduated 2017)
2.Nestor Nina Zarate (Graduated 2022)
3.Alexander Cantoral (Graduated 2024)
4.Gabriel Lacerda (Expected 2025)
5.Talita Santos de Araújo (Expected 2027)
6.Jônatas Marinho (Expected 2027)
MSc Students
1.Gabriel Lacerda (Graduated 2022)
2.Alexander Cantoral (Graduated 2020)
3.Juan Monges (Coadvisor - Graduated 2020)
4.Elkin Campos (Coadvisor - Graduated 2018)
Undergraduate Students
1.Flaisson Silva (Graduated 2024)
2.Gabriel Lacerda (Graduated 2020)
Publications:
Books
●Classical And Dynamical Markov And Lagrange Spectra: Dynamical, Fractal And Arithmetic Aspects, (with D. Lima, C. Matheus and C. Moreira), World Scientific, (2020 - Book), https://doi.org/10.1142/11965
Papers
1. Fractal dimensions of the Markov and Lagrange spectra near 3, (with H. Erazo, C. Moreira, R. Romo.), Journal of the European Mathematical Society, (2024), https://doi.org/10.4171/jems/1545
2. Rigidity of Lyapunov Exponents for Geodesic Flows, (with N. Nina), Journal of Differential Equations, 414, 125-142 (2025). https://doi.org/10.1016/j.jde.2024.09.004
3. Typical Conservative Homeomorphisms Have Total Metric Mean Dimension, (with G. Lacerda), IEEE Transactions on Information Theory, (2024) https://doi.org/10.1109/TIT.2024.3432658
4. A note on the density of periodic orbits of Anosov geodesic flow in manifolds of finite volume, (with N. Nina), Bulletin of the Brazilian Mathematical Society, New Series, 56(6), (2025), \\https://doi.org/10.1007/s00574-024-00427-2
5. Some Rigidity Theorems for Anosov Geodesic Flows in manifolds of Finite Volume, (with Í. Melo), Qualitative Theory of Dynamical Systems, 23(114), (2024), https://doi.org/10.1007/s12346-024-00972-7.
6. On the Lagrange and Markov Dynamical Spectra for Geodesic Flows in Surfaces with Negative Curvature, (with C. Moreira), Journal of Modern Dynamics, 19, 187-236, (2023), https://doi.org/10.3934/jmd.2023005.
7. Density of the level sets of the metric mean dimension for homeomorphisms, (with R. ~Arias and J. Muentes), Journal of Dynamics and Differential Equations, (2024), https://doi.org/10.1007/s10884-023-10344-5.
8. Geometric conditions to obtain Anosov geodesic flow for non-compact manifolds, (with A. Cantoral), Dynamical Systems - An International Journal, 1–18, (2024), https://doi.org/10.1080/14689367.2024.2345351.
9. On the Lagrange and Markov Dynamical Spectra for Geodesic Flows in Surfaces with Negative Curvature, (with C. Moreira), Journal of Modern Dynamics, 19, 187-236, (2023), https://doi.org/10.3934/jmd.2023005
10. H\"older continuous maps on the interval with positive metric mean dimension, \\ (with R. ~Arias and J. Muentes), Revista Colombiana de Matem\'aticas, 57, 57-76, (2023).
11. Hausdorff dimension and complex hyperbolic Schottky groups: a simplification, (with A.Ucan-Puc), Geometriae Dedicate, 216(58), (2022), https://doi.org/10.1007/s10711-022-00718-2.
12. On the Lagrange and Markov Dynamical Spectra for Anosov Flows in dimension 3, Qualitative Theory of Dynamical Systems, 21(19), (2022), https://doi.org/10.1007/s12346-021-00543-0.
13. Continuity of Hausdorff Dimension Across Generic Dynamical Lagrange and Markov Spectra II, (with C. Moreira and A. Cerqueira), Ergodic Theory and Dynamical Systems, 42(6), 1898-1907, (2022), https://doi.org/10.1017/etds.2021.18.
14. Contributions to the study of Anosov geodesic flows in non-compact manifolds, (with Í. Melo), Discrete \& Continuous Dynamical Systems, 40(9): 5149-5171, (2020), https://doi.org/10.3934/dcds.2020223.
15. Hausdorff Dimension, Lagrange and Markov Dynamical Spectra for Geometric Lorenz Attractors, (with C. Moreira and M. Pacifico), Bull. Amer. Math. Soc., 57: 269-292, (2020), https://doi.org/10.1090/bull/1657.
16. On the Lagrange and Markov dynamical spectra, (with C. Moreira), Ergodic Theory and Dynamical Systems, 37(5): 1570-1591, (2017), https://doi.org/10.1017/etds.2015.121.
