05/08/2020

Art inspires José Ezequiel in mathematics.

Mexican mathematician José Ezequiel Soto Sánchez draws his inspiration from the drawings of M.C. Escher and literature. “I am a great admirer of the artist, who worked extensively with tiling the plane and other surfaces. Gradually, I became interested in works on Islamic art and, at the Mathematics Festival in 2017 , I met researcher Asla Medeiros e Sá, who was preparing a publication of tilings inspired by her father's artisanal work,” says the IMPA doctoral student, who has been developing tools for constructing and visualizing patterns since his undergraduate studies.

Next Tuesday (11), at 11 am, he will defend the thesis “On periodic tilings with regular polygons”, under the guidance of Luiz Henrique de Figueiredo and co-guidance of Asla Medeiros e Sá, from the School of Applied Mathematics of the Getúlio Vargas Foundation (EMAp-FGV) by videoconference. There will be a broadcast on IMPA's YouTube channel .

“My research deals with periodic tilings of the plane with regular polygons,” examples of which are frequently found in kitchens and bathrooms. “ Regular squares, triangles, and hexagons tile the plane in a known way. In addition to these, a total of 11 tilings with only one type of vertex are known,” known as Archimedean tilings.

“There are also other vertices that do not tile the plane on their own, but can be combined to form tilings; in total there are 15 vertices. Fourteen of them can be combined in various ways. My research is related to the representation and construction of these more complex tilings . A simple representation based on integers was developed, through which it became possible to acquire and classify two large collections.”

Another highlight of the thesis is the solution developed to systematically enumerate and generate the tiling patterns. The method is unprecedented, and Ezequiel aims to publish it soon.

Ezequiel is Mexican, he grew up and lived with his family in Mexico City. “ It was a simple middle-class life, but we were always surrounded by opportunities to enjoy culture and sports. My parents frequently took us to museums, symphony concerts, the theater, or the cinema. At home, we had more than one encyclopedia to look up various topics, one of them with advanced content in English, which I've used since I was a child.”

The father of the future PhD in mathematics used to engage his children with mathematical riddles and problems during car trips. "He was very firm, he never revealed the answer." Yakov Perelman's book on recreational arithmetic was one of Ezequiel 's favorite pastimes , especially during summer vacations. "I also had very good math teachers. In my last year of high school, the subjects on specific topics in mathematics and calculus were very interesting. That year, I gave up on engineering altogether and had the support of my classmates to choose mathematics."

Before entering university, Ezequiel worked as a teacher in a volunteer project for a year in an indigenous community. The experience opened up a new field of possibilities in educational and social projects.

In 2005, he completed his studies in applied mathematics at the Autonomous Technological Institute of Mexico (ITAM), and immediately began his master's degree. "However, I ended up putting my academic career on hold for many years, dedicating myself to consulting work in data analysis for social research and to teacher training, curriculum development, and the creation of teaching materials with a federal institution for intercultural education in Mexico, CGEIB."

Eight years later, after moving to Brazil, he resumed his plans to pursue a master's degree. This time, in production engineering at UFRJ, where he dedicated himself to research in the field of education. “ After my master's degree, I decided to continue my studies, and that's when I learned about IMPA. I took the summer course and applied for the doctorate in computer graphics. I wasn't accepted at first. In August 2016, I was approved,” he recounts.

“At first it was a challenge, but I managed to get into the rhythm. The quality of the institute in its training, infrastructure, and research is extremely high.” For him, in addition to the mathematical learning, the networks formed in the academic environment, in educational events, and in communicating mathematics to the general public will remain. “Like the festivals, events such as IMPA Open Doors , the National Science and Technology Week … All of this has been very important to me. I also believe it was lucky that my time at IMPA coincided with the Mathematics Biennium , which allowed me to participate as a volunteer in the 2017 International Mathematical Olympiad (IMO) and the 2018 International Congress of Mathematicians (ICM) . IMPA also brought me closer to Livro Aberto , a very dear project with which I continue to collaborate. ”