21/02/2025

Thyago Souza: an itinerant mathematician at IMPA

With an academic career that spanned four regions of Brazil and included a period in Portugal, IMPA student Thyago Souza will defend, this Wednesday (26), at 10 am, his doctoral thesis “Well-placed and special solutions for local and non-local nonlinear dispersive models”. The work was developed under the guidance of researcher Felipe Linares. The defense will take place in room 232 of the institute and will be broadcast on IMPA’s YouTube channel.

Originally from São Paulo, Thyago began his undergraduate studies in mathematics at the Federal University of Sergipe (UFS). During his studies, he considered switching to physics, motivated by his interest in understanding natural phenomena. However, he was discouraged by a professor and, over time, realized that his true interest lay in the mathematics that underpins physics—especially mathematical analysis.

“I’m the type of person who needs to see to believe. There are many things that work in the realm of ideas, but are difficult to verify through calculations. And I like to verify, to do the math. And I realized, from the beginning, that mathematical analysis allowed for the verification of ideas through calculations,” explained the doctoral candidate.

In 2019, Thyago, who was the second in his family to complete higher education, moved to Minas Gerais and began his master's degree at UFMG (Federal University of Minas Gerais) focusing on the same area: mathematical analysis. Two years later, he arrived in Rio de Janeiro after being accepted into the doctoral program at IMPA. His application to the institute received a boost from his advisor at UFMG.

“My master’s thesis advisor, Luiz Gustavo Farah, was also a student of Professor Felipe Linares, and he strongly recommended that I come to IMPA. At first, I was a little reluctant. At the time, I didn’t feel like I was all that qualified to study here, but he insisted, and it was really great.”

At IMPA, Thyago also had the opportunity to pursue a sandwich doctorate. He spent a year at the Instituto Superior Técnico in Lisbon under the guidance of researcher Simão Correia. “He is a fantastic professor, so I worked intensely. Everything I did there was extremely valuable and, for sure, we became collaborators, as we still have a lot of work to develop. I co-authored a chapter of my thesis with him, a result of this period of joint research. It was a fantastic experience.”

Thyago's research investigates one-dimensional nonlinear dispersive equations using tools and methods from partial differential equations and harmonic analysis, with a particular focus on models for long internal waves influenced by Coriolis forces and the Benjamin-Ono equation with generalized dispersion.

“For models influenced by the Coriolis effect, we established local and global well-placedness in low-regularity Sobolev-type spaces, in which rotational effects are represented by a non-local operator. For Benjamin-Ono-type equations with generalized dispersion, we obtained optimal well-placedness results and analyzed several qualitative properties of the solutions, including long-term behavior, scattering and explosion criteria, among others.”

With an academic career that includes a little over 7,000 kilometers of travel, Thyago is preparing for a new challenge: soon, he will travel to Campinas (SP), where he will begin his post-doctoral studies at Unicamp.