16/07/2019

From budding astronomer to IMPA researcher

Reimundo Heluani's childhood dream was to be an astronomer. Inspired by the television series "Cosmos" by the American scientist Carl Sagan (1934-1996), the Argentinian boy imagined he would pursue that career. Since dreams don't always come true, he became a mathematician. Today, at 41, he is an associate researcher at IMPA, specializing in Algebra.

At age 8, Heluani received his first computer, a Commodore 64C. “I already had some experience programming my mother’s Texas Instruments. But learning to program in BASIC was fascinating. At 12, I got my first PC, an XT-8088, without a hard drive. My mother was taking a course at the university. I could go to the lab to play and follow her course. That’s where I learned to program in Assembler. At the time, my dream was to program a sophisticated virus.”

Heluani was born in Tucumán (northwest Argentina). At age 5, his family moved to Córdoba. Besides him, the family consisted of his parents (Ricardo and Silvia), his brother Nicolás, and his younger sister Nayla. In 1989, the family returned to Tucumán. “I finished elementary school in a public school. I completed high school at a university institute similar to the Colégio de Aplicação of the Federal University of Rio de Janeiro.”

The student practiced sports: tennis from ages 5 to 10, taekwondo, and high jump. Mathematics came into his life in high school, when he participated in an olympiad. “This had profound consequences in my life. To this day, my closest friends are colleagues from the Argentine Mathematical Olympiad.”

Heluani believes she pursued a career in mathematics due to family influence. “It seems strange, since my father is the only one without a university degree. He left college when I was born. He was 21 years old and a traveling salesman. However, I believe it was a great influence. I say it seems strange because my mother and one of her sisters are physicists. Another sister is a mathematician. So, it comes from the family.”

The researcher reports that financial issues contributed to the choice. “What finally made me switch from Physics to Mathematics may have been money. I left Tucumán to study Physics in Córdoba. I lived alone, money wasn't plentiful. But my family could support me, I didn't need to work. That made a big difference compared to many friends who couldn't finish [their degree].”

Heluani recounts that in her second year of college she learned about monthly scholarships of US$330 in the Mathematics course. “So, I did both degrees. I was studying general relativity in Physics and working with Lie algebra representations in Mathematics. I started my PhD in Physics. But the country's economic situation, at the end of 2001, beginning of 2002, deteriorated very rapidly. I had good offers to do my PhD in Mathematics in the USA.”

The researcher completed his undergraduate degrees in Physics and Mathematics in Argentina and his doctorate in Mathematics at MIT [Massachusetts Institute of Technology, USA]. He was also a Miller Fellow, with a postdoctoral fellowship, at the University of Berkeley, California.

"At MIT, I taught summer classes to students from so-called minority groups, who would enter the following year in worse conditions than the others."

IMPA is praised by the researcher, who believes its students, "on average, leave little to be desired compared to students from very good institutions in the US," and that there is "freedom to research any topic."

“We can offer interesting courses on topics of our choosing. We have excellent students, facilities for bringing in international collaborators, and opportunities to travel abroad for conferences. The salary is very good by national standards and was once quite competitive by international standards.”

In her work at IMPA, Heluani uses geometry to explain algebraic objects. “When you imagine a Rubik's Cube, 3x3x3 with six colors on its faces, you already have a geometric idea in your head. There are operations to rotate one of the sides 90 degrees. If you do the same rotation four times, nothing changes in the cube. The image can be very good for someone trying to visualize the cube or for a child trying to solve the problem of making all six faces the same color.”

Heluani states that, “for a computer, it’s better to think in terms of 20×20 matrices with real number entries. There is a matrix for each operation on the cube. Performing two operations in a row corresponds to multiplying the matrices. For example: for a 90-degree rotation, there is a 20×20 matrix that 'represents' it.”

The researcher explains that the area of mathematics that studies abstract structures (the symmetries of the Rubik's Cube and the sidewalks in Copacabana, for example), replacing them with matrices, is the theory of representations. "I work with infinite x infinite matrices. For this type of structure, the geometric view – the cube in your hands, for example – can sometimes be better suited to a computer."