Geometric analysis allows us to understand space and model structures efficiently

In a four -dimensional world, geometric analysis allows us to better understand the space in which we live and model structures efficiently. In the construction of bridges, buildings or aircraft design, this discipline is keyRaquel del Carmen Perales Aguilar, researcher at the Center for Mathematical Sciences (CIMAT) in Guanajuato, will celebrate that in Mexico there is a rise of master’s and doctorate students interested in that discipline.

In an interview with The dayexplained that More and more Mexican young people are interested in geometric analysis, a field of mathematics that combines differential equations with the study of the geometric properties of objects. It is an expanding field in our country.

The doctor from the University of Stony Brook considered that this growth is due to recent advances. Especially because this discipline also has applications in artificial intelligence, especially in the machine learningwhere it helps improve the representation of data in multidimensional spaces, optimizing the ability of computers to learn and improve their performance without explicit programming for each task.

However, he clarified that many of the advances are theoretical and do not always have an immediate application. “But pure and applied mathematics are always feedback. Questions that seem abstract today can be the key to solving future problems in physics, engineering or technology.

The resolution of some mathematical questions or conjectures could be on their way to solve the millennium problemshe added.

Mathematics students, Raquel Perales recommends keeping curiosity alive. It is fundamental. Explore different areas of knowledge, that is very important, because one never knows at what point they will be mixed and, often, those mixtures are usually very productive.

Perales Aguilar was interested in geometric analysis almost at the end of his degree. When it was time to choose the theme of his thesis, one of his mentors brought him a topology book by John Milnor, whose contributions have been recognized with the Fields Medal (1962) and the ABEL Award (2011).

“I took it in my hands and barely leafed through it, I was captivated: I saw things of calculation and geometry. I didn’t know much about what was in the book, but I liked the images, the symbols I saw, and I said: ‘I want to learn this kind of thing’. ”

By entering her research work, the mathematical scientist has discovered several interesting edges, but has focused on problems related to the general theory of relativity.

When we do science, we try to build simple models to represent reality. We can imagine the earth as a perfect sphere, but in reality its surface is irregular, with mountains and valleys. Geometric analysis helps us describe and understand those complexitiessaid the researcher.

As the study of these phenomena becomes more complex, he reiterated, it is necessary to combine different areas of knowledge. Before, each discipline operated independently, but today interdiscipline is fundamental. In the geometric analysis, we combine differential equations with the study of geometric structures to solve problems from various areas.