13/03/2018

Roberto Alvarenga 'dreams' of an application for his research.

Specialist in algebraic geometry, an area of Mathematics that combines techniques of abstract algebra with the language and problems of geometry, Roberto Carlos Alvarenga Júnior defends this Tuesday (13), at 1 pm, at IMPA, the doctoral thesis "Hecke operators and Hall algebras for global function fields".

Alvarenga Júnior found his calling in mathematical research. He is not concerned about whether his work will have an impact or application. He knows that Pure Mathematics requires time to find a place in people's daily lives, although it is part of the daily routine of the "crazy ones"—as he himself defines them—who choose the profession.

In his thesis, the author works with automorphic forms and Hecke operators. His proposal is precisely to describe certain graphs that parameterize the action of these operators in automorphic forms.

The mathematician knows that it's not an easy topic to explain to the general public, especially since there's no everyday application. The closest example is the use of this knowledge in security keys for systems, such as those created by banks.

"Personally, I think every mathematician dreams one day that their work will have applications. But, in my case, from the beginning, that real-world application wasn't very clear. It's very pure mathematics," he confesses.

Born in Jales, in the interior of São Paulo state, Alvarenga Júnior reveals his pride in completing his doctorate at "a center of excellence" like IMPA.

“I don’t need to advertise. It’s enough to highlight all the people who are here, the fact that I’m organizing the next ICM, and that we have excellent researchers and professors.”

The doctoral candidate, who completed a sandwich master's program in France, says that the time he spent in Europe provided personal and professional growth. There, he realized that IMPA is on par with the world's leading centers of excellence in elite mathematics.

For the student who was the only algebra specialist at Unesp in São José do Rio Preto, studying at IMPA was essential for having someone to exchange ideas with about the field of mathematics. "There are very good researchers here. They were all fundamental to my education," he says.

Alvarenga Júnior was mentored in Brazil by Oliver Lorscheid and in France by Oliver Schiffmann of the University of Paris XI. After defending his thesis, his next commitment is marriage. After his honeymoon, he will return to the state of São Paulo to do his post-doctoral studies in São Carlos. This will mark the beginning of his research career.

SERVICE:

Defense of thesis by Roberto Carlos Alvarenga da Silva Júnior

"Hecke operators and Hall algebras for global function fields"

Date: March 13th | Time: 1 PM | Location: Room to be determined