16/02/2024

Between Mathematics and Physics, Felipe defends his doctoral thesis.

In a few days, Felipe Espreafico will turn 26 and that's not the only reason to celebrate. Next Friday (23), he will defend his doctoral thesis ' Modularity and Enumerative Geometry of Physical Invariants', at 10:30 am in room 232. The presentation can also be followed on IMPA's YouTube channel.

From Ribeirão Preto (SP), Felipe has always had an affinity for the field of exact sciences and has won bronze medals in the Brazilian Chemistry Olympiad and the Brazilian Physics Olympiad. And a silver medal in the São Paulo State Chemistry Olympiad.

While torn between pursuing mathematics or physics, he realized through his interactions with friends that he had a way of seeing things from a mathematical perspective.

"It was in my final year of high school that I decided on mathematics because I realized it offered a different perspective, one more focused on the theoretical aspects," said the doctoral student.

Another thing Felipe enjoys is the dialogue, the exchange of ideas about mathematical problems in order to arrive at a solution. "Many people asked me if college was going as I expected, and my answer was no. Because mathematics at a more advanced level is more rigorous," he said.

As the first mathematician in his family, Felipe is the son of university professors focused on molecular biology. He says this makes all the difference in his career because, although his parents don't understand exactly what he does, they have an understanding of the stages of research and development, allowing them to follow along and provide greater support.

A graduate in Mathematics from USP São Carlos, the young man decided not to pursue a master's degree and went straight into a doctoral program after being accepted at IMPA in 2020. Throughout his undergraduate studies, he was already involved in scientific research, including spending time in Germany.

These undergraduate research projects were essential in giving me an idea of how research worked. "If I had chosen to do a master's degree, I would have ended up repeating some of what I had already learned in these undergraduate research activities."

Supervised by IMPA researcher Hossein Movasati, Felipe's thesis explores the relationship between mathematics and string theory, a branch of physics. The first half of his thesis takes enumerative invariants (that is, counts of geometric objects) that already existed in physics and brings them into a more geometric and modular context, essentially a geometrization of these counts. The other part of the work considered ways to refine these invariants, relating them to arithmetic in some simple examples.

During his doctoral studies, he had the opportunity to return to Germany, where he studied for 10 months with a CAPES scholarship at the University of Heidelberg in 2022.

“I went to continue work I was already developing at IMPA, but in Germany we started discussing things that were a little different. I was interested in interpreting the counts as modular forms, but there I also became interested in how to better interpret the counts themselves, analyzing refinements and generalizations,” he said.

In Germany, Felipe was able to look at these types of counting in a more general way, spending part of his stay focused on understanding possible ways to refine them. “We didn't prove anything new, but we showed relationships between more concrete examples from Physics and Mathematics, creating connections that no one had paid attention to before. It was a work that was very well received by the community.”

Upon completing his doctorate, Felipe will pursue a postdoctoral fellowship at the Sorbonne University in Paris, France, fulfilling his desire to return to Europe, both for the academic experience he has already gained there and for personal reasons. "I'm familiar with the environment and I've started dating a German woman," he said.