25/09/2023

'Mathematics has brought me many good things,' says doctoral student.

Born in Santa Cruz, Bolivia, Diego Salazar Gutierrez came to live in Brazil to study and fell in love with Rio de Janeiro. For the IMPA doctoral student, the best parts of living in the city are the beaches, the food, and the tourism. “Brazil has an excellent level of mathematics, and I really liked Rio de Janeiro. In addition, Santa Cruz is similar to Brazil; it's also very hot and has many Brazilians. These were also factors that made me come here,” he said.

This Tuesday (26), Gutierrez takes another important step in his academic career. He defends the thesis “PBW bases of irreducible Ising modules”, at 10 am, in room 232 at the institute, with live broadcast on IMPA’s YouTube channel . In the work, supervised by IMPA researcher Reimundo Heluani, Gutierrez presents an algebraic application of the Theory of vertex algebras with the aim of addressing the concept in a more concrete way.

He details that for each h+N-graded module M over an N-graded vertex algebra V, there is associated an increasing filtering (G^pM), which is compatible with the filterings introduced by Haisheng Li. The associated graded vector space gr^G(M) is naturally a module over the Poisson vertex algebra gr^G(V). With this, he obtains an explicit PBW basis for each of these modules and a formula for their refined characters, which are related to Nahm sums for the matrix [[8, 3], [3, 2]].

"My work is a concrete application of the theory of vertex algebras. Often mathematics is abstract, it doesn't have examples, I think that's bad. Whenever there's a concept, there should be examples, so my work follows a more concrete line," he explained.

A graduate of the Universidad Mayor de San Simón in Cochabamba, Bolivia, Gutierrez came to Brazil to pursue a master's degree at the Federal Fluminense University (UFF) and later a doctorate at IMPA. "I really like IMPA. The teaching here isn't monotonous, and it's not complicated to learn either. I've made good friends, and the professors are excellent. I will definitely return to the institute many times, even if only to visit."

Interested in mathematics since childhood, the student even participated in some competitions during his high school years. The choice of career came naturally. "It's a lot of work, but I believe I've done well so far. Mathematics itself has brought me many good things."

The young man has two brothers, who also live abroad, one in Germany and the other in Australia. The doctoral student's parents live in Bolivia and have learned to cope with the distance. "They are happy and satisfied with my work. With all the children abroad, I am the closest one, it's only a four-hour flight."

The student says that his next steps include a postdoctoral fellowship in Brazil, a country where he feels welcomed and happy. "I don't know if I'll stay in Brazil forever, but for now I want to continue here. There are very good postdoctoral opportunities in Rio, but I'm also thinking about going to São Paulo."