28/03/2025

'OBMEP was my first contact with mathematics,' says Fazoli.

“My first contact with mathematics was with OBMEP”. The Olympiad was the initial chapter of the success story that IMPA doctoral student Gabriel Fazoli is writing with mathematics. The seven gold medals won by the young man preceded other achievements in the area, such as the defense of his doctoral thesis at IMPA this Thursday (27). The project “Planar partial connection jets” was supervised by researcher and deputy director of IMPA, Jorge Vitório Pereira, and the defense can be followed on IMPA's Youtube channel.

Originally from Urupês, in the interior of São Paulo, Gabriel holds a degree in mathematics from the São Paulo State University Júlio Mesquita Filho (UNESP) – Ibilce campus, in São José do Rio Preto – and a master's degree from IMPA. During his undergraduate studies, Gabriel also reaped the benefits of his involvement with OBMEP as a scholarship recipient of the Scientific Initiation and Master's Program (PICME). This was just one of the opportunities that the public school student says he had access to through the Olympiad. The first and most important of them was his passion for mathematics.

“Ever since I learned about OBMEP, when I started participating in the Olympiad, I've had a greater, different interest in mathematics. I got involved in several other Olympiads. At some point, it also became natural to want to pursue mathematics as a career; at some point in that journey, I thought, 'Well, I want to do mathematics, I think it's a good idea.'”

A gold medalist in all seven editions he participated in, Gabriel was also a student in the Junior Scientific Initiation Program (PIC) for six years, participated in the Hilbert Hotel Meeting and the national award ceremonies. Of all the opportunities offered by the Olympiad, the student highlights his participation in the PIC as an incentive to pursue a career in mathematics. “The program allowed me to mature mathematically a little earlier. I was exposed to mathematical concepts much sooner than expected, which was very good for me.”

The chosen topic for my doctoral research was Holomorphic Foliations, an interest that arose during my master's degree. Basically, a foliation is the decomposition of a space into a set of submanifolds, called leaves, which locally are solutions to a system of differential equations. The field focuses on the study of these leaves and their geometric properties.

“I liked this concept of foliation because it's an area that intersects with other areas: Algebraic Geometry, Complex Geometry, Topology, Riemannian Geometry, all within the concept of foliations. I've always been interested in different areas of mathematics, and in foliations all of this appeared naturally, in diverse contexts. We were able to apply the results from all these other areas to foliations.”

In his doctoral studies, the young man studied partial connections, which is a generalization of the concept of connections from Riemannian Geometry to the area of foliations. In general, a partial connection is a way of defining the derivation of algebraic and geometric objects in directions tangent to the leaves. "My research has basically focused on studying partial connections, jets of partial connections, and applying this to some classic problems in the area of holomorphic foliations."

Looking to the future, Gabriel plans to pursue a postdoctoral fellowship in Bari, Italy, alongside researcher Maurício Correia (University of Bari). His expectations are positive, just as they were when he decided to join IMPA in 2019. “What motivated me to come to IMPA is that, as IMPA is an international center for mathematics, in a sense, we have much more interaction with researchers from various fields and places. It’s great to be in this environment that provides contact with international researchers and the opportunity to participate in many conferences.”