Here is my current CV (February 2024).
I am a mathematician working on elliptic and parabolic partial differential equations, more specifically in the analysis and regularity aspects of these equations. My contributions also include analysis of integro-differential operators, free boundary problems and calculus of variations. In my research I have developed estimates for solutions of differential equations based on classic geometric ideas such as maximum principles, Harnack's inequalities and regularity by compactness. The fundamental questions and insights for these problems are motivated in physical and social sciences, probability, geometry and optimization.
I have been fortunate to have learned and shared mathematics with mentors and friends in different places during my career such as Venezuela, the United States, and Mexico. I am passionate about teaching and have mentored a few students and postdocs at Centro de Investigación en Matemáticas, the Mathematics Department at the University of Guanajuato and highschool students for the Asociación de Competencias Matemáticas Venezolanas. I welcome students of any levels and disciplines related to mathematics to contact me about research projects in modelling and analysis of differential equations, either for short term summer programs, MS and PhD theses, or postdoc sponsorships. A good place to start learning what we could be working together is taking a look at some of the workshops that I have taught recently. You may also take a look at some of the theses and projects I have mentored.