01/04/2019

Miguel Ibieta defends thesis on Euclidean subvarieties.

Despite having a mother who was a mathematician and a father who was an engineer, Bolivian Miguel Ibieta Jimenez never felt pressured to pursue a scientific career. From the beginning, his love for numbers came naturally. Through participation in local olympiads, where he won several awards, he realized it was more than just an interest; he wanted to delve deeply into mathematics.

This Tuesday, Ibieta will share the results of his immersion research with the defense of his thesis, “Genuine infinitesimal bendings of Euclidean submanifolds,” at 10 am at IMPA.

Up high

Perhaps it was because he grew up in Potosí, one of the highest cities in the world (4,067 meters above sea level), that Ibieta was never destined for low-level flights.

Upon completing his undergraduate degree in Mathematics at the Universidad Mayor de San Andrés (UMSA) in 2013, Ibieta boarded a plane that same year bound for Rio de Janeiro. He began his master's degree at the Federal Fluminense University (UFF) in Niterói (RJ), and soon after, he came to IMPA for his doctorate.

Ibieta reveals that, although she had liked mathematics since childhood and wanted to pursue a career in the field, it was only when she set foot in college that she discovered its true meaning.

“Mathematics is important on a practical level, but also in a more abstract way, since the rigor of the discipline makes us more critical. In the field of exact sciences, for an argument to be valid, we need to verify all the details, check if the logical process of things has no flaws. These aspects can be adapted to everyday life, making us think more about what we say and hear. That is why we should stimulate people's interest in the discipline,” he said.

Revisiting a classic

Situated in the area of Differential Geometry, Ibieta's thesis discusses a notion of deformation of submanifolds of Euclidean space.

A basic example of these deformations can be observed by taking a sheet of paper and transforming it into a cylinder, without folding or tearing it. The intrinsic geometry of the sheet of paper remains the same. What Ibieta studied was an infinitesimal version of this type of deformation.

“It’s a classic subject. The first works in this area were done at the beginning of the last century. My advisor proposed the topic, I accepted, and it simply flowed,” he recalls. He adds that he received a lot of support from Marcos Dajczer, which made the experience of developing the thesis even better.

When asked about his plans after the defense, Ibieta jokes: "I'm going to face unemployment." Immediately afterwards, he reveals his true intention: he plans to pursue a post-doctoral degree.

SERVICE:
Defense of thesis by Miguel Ibieta Jimenez
“Genuine infinitesimal bendings of Euclidean submanifolds”
Date: April 2nd | Time: 10:00 AM | Location: Room 228