Students Present Research Projects in France

Students Thiago Vinicius Alves and Yasmin Monteiro, who are pursuing a bachelor’s degree in Mathematics in the Technology and Innovation program, presented a research project as part of the EUR MINT 2026 Summer School: Particle Systems and PDEs, held June 15–19 at the Institut de Mathématiques de Toulouse (IMT) in France. Supervised by Professor Milton Jara, the research marks the first time IMPA Tech undergraduate students have participated in an international academic event held outside Brazil.

Recognized for bringing together researchers and young scientists in the field of Probability and Partial Differential Equations (PDEs), the summer school focused on the relationship between stochastic models of particle systems and their macroscopic descriptions via partial differential equations. In addition to lectures and mini-courses, the program included poster sessions and scientific presentations by participants from different countries. Although the event’s audience consisted mainly of master’s and doctoral students, postdocs, and early-career researchers, the young scholars had the opportunity to present their results and discuss their work with experts.

The research was conducted throughout this year as part of the Scientific Initiation and Master’s Program (PICME), designed for college students who excelled in the Mathematics Olympiads (OBMEP or OBM medalists). The study investigated modifications to Smoluchowski’s coagulation equations, a mathematical model used to describe systems composed of particles of different masses that coalesce over time to form larger particles. The goal was to find adaptations of the equation that would allow for the identification of steady-state solutions—configurations that remain unchanged as the system evolves.

As a result, the students identified three variations involving different ways of injecting particles of mass 1 into the system and observed that the steady-state solutions obtained are related to classical recurrence relations in combinatorics, such as Catalan numbers.

The opportunity to present the work arose through a recommendation from Professor Milton Jara to submit it. The poster proposal was approved, and the University of Toulouse provided financial assistance for the young Brazilians to participate in the Summer School.

For Yasmin Monteiro, the event represented a unique opportunity to share her research and gain firsthand insight into scientific work being conducted in other countries. “It was a very enriching and rewarding event. We had the opportunity to meet researchers, master’s students, and doctoral candidates from all over the world. In addition, we attended lectures, viewed posters from other projects, and participated in mini-courses related to probability,” she said.

One of the moments that left the greatest impression on the student was her interaction with researchers who work directly on the topic being investigated by the group. “One of the mini-courses was specifically about Smoluchowski’s equations. Researcher Luisa Andreis took a keen interest in our work and offered some very interesting suggestions on how we could continue the research.”

For Thiago Vinicius Alves, the trip also had personal significance: it was his first international experience. “I had never left Brazil before, and I was very curious to see what was similar or different about how math is taught abroad.”

The student says he was surprised by the audience’s positive response to the work he developed during his undergraduate studies. “Since the event was mainly for master’s and doctoral students, I didn’t expect our poster to get so much attention. It was really cool to see people interacting, asking questions, and wanting to take pictures of the poster.”

According to Thiago, the experience reinforced his interest in an academic career. “Attending the presentations and mini-courses showed us the variety of paths that research can take. We also had the opportunity to talk with leading figures in the field, who reflected on our results and suggested new problems for us to study.”

Thiago and Yasmin’s participation in the EUR MINT 2026 Summer School marks a milestone for IMPA Tech by expanding the international reach of its research. This experience demonstrates how undergraduate research projects can create opportunities for academic advancement even while students are still in college.