03/04/2023

'Mathematics is my profession and my hobby,' says doctoral student.

It was during his third year of high school, when he became a teaching assistant at the school, that 27-year-old Brayan Cuzzuol Ferreira decided he would make mathematics his profession. His interest in the field arose through a teacher who decided to present the subject in a different way – far from the rote memorization of formulas and theorems, a common practice in schools. Another teacher was responsible for the student's first job in the field of exact sciences. These new experiences led Brayan to abandon the idea of studying statistics. The natural path was to pursue mathematics.

Ten years after the decision, the current IMPA student presents his doctoral thesis: “Immersed contact homology and the 2-sphere” under the guidance of Vinícius Ramos, a researcher at the institute. The defense is scheduled for 12 pm, this Tuesday (4), in room 232, and will be broadcast on IMPA's YouTube channel .

In his work, the doctoral candidate addresses symplectic geometry, an area of mathematics that studies geometric objects equipped with a structure capable of measuring the sizes of two-dimensional objects. This structure originates from the Hamiltonian formulation of classical mechanics and allows the study of the dynamics of a mechanical system.

“In my thesis, we focused on the cotangent bundle of the two-dimensional sphere, which can be interpreted as the set of points and moments, in the physical sense, on the 2-sphere. Here, the two-dimensional 2-sphere means a set of points having the same distance from a given point in three-dimensional space. Using a theory called embedded contact homology and integrable systems theory, I studied the embedding of other geometric objects within this cotangent bundle in such a way that the symplectic structure was preserved,” he explained.

Originally from Espírito Santo, Brayan completed his bachelor's degree in mathematics at UFES (Federal University of Espírito Santo) in 2017. Initially, the young man intended to complete a teaching degree, but once again a professor intervened and convinced the then-university student to enroll in some bachelor's degree courses, which later led him to the research field.

“I enrolled in the mathematics course thinking about working in basic education, since I had the opportunity to work as a teacher in some schools and I really enjoyed it. However, when I was halfway through the course, Magda, a professor at UFES who was the head of the department at the time, suggested that I enroll in bachelor's degree courses. At that time, she, who had already been my professor in two courses, observed that I had the profile for the academic field and pure mathematics,” says the doctoral student.

Previously, during his master's degree (UFES), Brayan said that the encouragement for him to study at IMPA, where he began his doctoral studies in 2019, also came from professors. For him, the most fascinating thing about mathematics is the challenge.

"I find it very interesting that we can describe and understand some phenomena using mathematical language, and I think that's one of humanity's greatest challenges. I believe that mathematics is one of the greatest assets for the development of society."

Looking to the future, Brayan aims to become a university professor, continuing his research. “I love learning, but I also love teaching. So, doing both of these things is my biggest goal. Mathematics is primarily my professional life, but sometimes I consider it a hobby as well,” concluded the doctoral candidate.