21/08/2019

Miquel Ten defends thesis on Poisson geometry.

Before arriving in Brazil five years ago, Spaniard Miquel Cueca Ten didn't expect to like the country so much. The image portrayed abroad wasn't the most positive. But upon setting foot in Rio de Janeiro, he realized it was a special place. He felt at home.

IMPA doctoral student Miquel begins, this Thursday (22), to say goodbye to the country that welcomed him. In room 232, he will defend the thesis “Applications of graded varieties in Poisson geometry”, at 2 pm.

A home away from home

Born in Valencia, Spain, Miquel found the warm familiarity of his hometown on the beautiful beaches of Rio de Janeiro. Having spent his childhood by the sea, accompanying his parents, who owned a bar, the mathematician grew up leaving footprints in the sand.

The familiar environment he's accustomed to is about to change. After defending his thesis, Miquel is embarking on a postdoctoral fellowship at the University of Göttingen in Germany. "It's going to be a challenge. I'll be studying in a small town without a beach," he jokes.

Geometer Miquel defines his field of work as an intersection of differential geometry and mathematical physics. With a master's degree from the University of Valencia, one of the oldest and most important in Spain, the mathematician recounts that the path leading up to his choice to pursue this research area was marked by uncertainty.

“I chose Mathematics quite late. I always had doubts about what to study, but I knew it had to be something that would allow me to tackle difficult questions. For a moment, I considered studying History, but, on the eve of the university entrance exam, I ended up deciding on Mathematics, as I found it a bit more objective.”

Despite having good teachers and a natural curiosity, Miquel says he received no direct influence to pursue this field. It was in his first year of college that he really started to get excited about it.

“At that time, two things happened. I failed analysis and, at the same time, I got the highest grade in the class in algebra. So I thought: 'maybe I'm not so slow, maybe I'm good at math',” he recalls.

At the end of his third year, he began to get involved in a scientific initiation project, developed with Professor Marco Zambon, at the Institute of Mathematical Sciences (ICMAT) in Madrid.

"It was Professor Zambon who introduced me to the study of symplectic geometry. At the end of the course, he recommended that I ask IMPA researcher Henrique Bursztyn, who works in the field, if he would be willing to supervise more doctoral students."

Under Bursztyn's guidance, Miquel wrote a thesis on Poisson geometry. “He was very patient with me. I am very grateful; I learned a lot. The important thing about Poisson geometry is that, beyond the internal problems of the area, there are connections with many other fields of mathematics. For someone starting out, it is very difficult to have this global perspective. Bursztyn always knew how to convey all these connections and relationships, a task that is not easy,” he says gratefully.

Poisson geometry has been used since the early 19th century to study classical and celestial mechanics, such as the solar system. With the quantum revolution in the following century, atomic physics had to deal with two types of particles: bosons and fermions.

“Since Poisson geometry can only deal with bosons, a new geometry emerges, supergeometry, which encompasses both bosons and fermions, allowing us to do classical mechanics with quantum particles. My study is at this intersection of problems that sometimes come from Physics,” he explains.

Miquel quotes the Russian mathematician Vladimir Arnold (1937-2010) to illustrate the importance of this intersection. “Arnold said that 'Mathematics is the part of Physics where experiments are cheapest.' What motivates me is that, broadly speaking, our projects have applications in Physics and we are working with an approximation of reality.”