IMPA doctoral thesis wins award at SIBGRAPI 2021
Defended in August 2020 by IMPA alumnus José Ezequiel Soto Sánchez, the thesis “On periodic tilings with regular polygons” was awarded best doctoral thesis in computer graphics at SIBGRAPI 2021 ( 34th Conference on Graphics, Patterns and Images ). Organized by the Brazilian Computer Society (SBC), the event is the most important in the field in Brazil, and took place virtually between October 18th and 22nd. The abstract of the thesis, supervised by Luiz Henrique de Figueiredo, from IMPA, and co-supervised by Asla Medeiros e Sá, from the School of Applied Mathematics of the Getúlio Vargas Foundation (EMAp – FGV), is available at this link .
The work depicts and constructs highly complex tiling patterns, and was presented again by Ezequiel, a native of Mexico City, at SIBGRAPI 2021. The presentation is available on the mathematician's YouTube channel. He was awarded the title of "Best Ph.D. Thesis Award of the Workshop of Theses and Dissertations (WTD)" at the event.
“Receiving an award like this encourages me to continue striving in my research work and is a source of great joy. It has been a great experience to address the problems of combinatorial geometry using a computational approach, while relying on the visual support of computer graphics tools, which allows us to appreciate the beauty of the resulting images. The recognition extends to my advisors Asla Medeiros e Sá and Luiz Henrique de Figueiredo, to the professors of the computer graphics program, and to IMPA,” celebrates Ezequiel.
To develop the work, the Mexican researcher addressed periodic tiling of the plane with regular polygons, examples of which are frequently found in kitchens and bathrooms. “Square tiles are an example of simple tiling. 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,” he states.
Ezequiel's thesis presents a simple representation based on integers, through which it was possible to acquire and classify two large existing collections of 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 novel, it appears in the thesis, and my intention is to publish the results soon,” the author points out.
Another important recognition of Ezequiel's thesis was the "committee highlight" in the Odelar Leite Linhares Award , granted by SBMAC (Brazilian Society of Applied and Computational Mathematics).
The thesis resulted in three other articles, which were presented at international conferences and published in traditional computer graphics journals. The articles are available at this link .