23/06/2021

Thesis by Mexican Ezequiel Soto wins SBMAC award.

Crédito: Arquivo Pessoal

The doctoral thesis of Mexican José Ezequiel Soto Sánchez , defended at IMPA in August 2020, was recognized as a "committee highlight" in the Odelar Leite Linhares Award , granted by SBMAC (Brazilian Society of Applied and Computational Mathematics). In "On periodic tilings with regular polygons ," the former IMPA student represents and constructs highly complex tilings. Supervised by Luiz Henrique de Figueiredo and co-supervised by Asla Medeiros e Sá (FGV EMap), the thesis develops a novel solution for systematically enumerating and generating tilings.

“I received the news with great joy. Winning an award like this is always an incentive to continue striving to produce quality research. It is not only recognition for me, but for the entire ecosystem that made my doctorate possible and encouraged me to carry out my work. It is also recognition for my advisors, for the professors of the computer graphics program, and for IMPA,” celebrated Ezequiel, who is currently doing a postdoctoral fellowship in geometric modeling and processing for scientific visualization at the Tecgraf Institute, at PUC-Rio.

With this achievement, he earns exemption from the registration fee to participate in the National Congress of Applied and Computational Mathematics (CNMAC) 2022, scheduled to take place in Porto de Galinhas (PE).

The award-winning thesis discusses periodic tiling of the plane with regular polygons. "Simple tilings, formed by squares, can often be found in kitchens and bathrooms," Ezequiel exemplifies. "Besides squares, regular triangles and hexagons tile the plane in a known way. However, squares, triangles, hexagons, and dodecagons can be combined in multiple ways of increasing complexity."

In his work, Ezequiel presents a simple representation based on integers, through which it was possible to acquire and classify two large collections of existing tilings, representing the state of the art on the subject to date. “Furthermore, I develop a solution for enumerating all tilings with triangles and squares. The number is infinite, but there is a way to enumerate and generate them systematically. The method is unprecedented, it appears in the thesis, and my intention is to publish the results soon,” the author points out.

“It is a very old and difficult problem, to which Ezequiel contributed with an elegant computational representation and a robust acquisition method, which allowed us to represent all known tiling patterns,” emphasized Figueiredo, the thesis advisor. “It was a great pleasure to supervise such a beautiful thesis, which combines classical mathematics with elegant computation and advances the state of the art also through the publication of data and algorithms, in addition to articles in good journals.”

The thesis resulted in three articles that were presented at international conferences and published in high-quality journals, among the most traditional in computer graphics. They are available at this link .