17/09/2019

The intersection between Computer Science and Mathematics

When she was in high school at CEFETEQ in Rio de Janeiro, Taísa Martins was satisfied with the precision of the answers to the questions posed by her teachers in the exact sciences. The process of studying content and applying it to then arrive at a correct or incorrect result was something that pleased her. It was black and white, and there was no room for ambiguity, unlike in the Portuguese language exercises, which the student found more difficult.

Perhaps her appreciation for this type of precision led her to approach the field of Mathematics to which she dedicates herself today. In her postdoctoral studies at IMPA, under the supervision of senior researcher Robert Morris, the specialist in extremal and probabilistic combinatorics is developing a project that seeks to understand the behavior of small substructures in large structures and what can be inferred about some sufficiently large systems.

Taísa's interest in the field began when she was doing her doctorate at the University of Warwick in England. The country is considered the birthplace of extremal combinatorics and has a community of scholars in the subject. "When I was there, I attended many seminars and conferences, and developed a strong interest in the area," says the Rio de Janeiro native, who returned to Brazil determined to pursue postdoctoral studies in the field.

A subfield of combinatorics, extremal combinatorics studies the relationships between various numerical parameters of discrete structures. In general, it answers questions such as how large or how small a certain parameter can be, given a condition on another parameter. "I really like the types of problems in this niche of mathematics because they are simple to describe and generally have ingenious solutions," says Taísa.

Raised on Ilha do Governador, the IMPA postdoctoral researcher grew up believing she would become a pharmacist and was enrolled in the Pharmacy technical course offered by the school. The approaching university entrance exams made her rethink her plans and begin to evaluate her undergraduate options in Physics, Mathematics, or Computer Science.

Reading the mystery novel "Digital Fortress" by British author Dan Brown sparked her curiosity about cryptography. Although it was a superficial exposition of the subject, the book captivated her with its intriguing narrative. Following her intuition, Taísa enrolled in the Computer Science course at the Federal University of Rio de Janeiro (UFRJ).

"At the beginning of my undergraduate studies, my dream was to work at Google." The American multinational represented the most modern and advanced aspects of the technology industry. She points out that "this was a common desire among students in the course at the time."

Taísa even interned at a company that developed software. But, as she absorbed the course content, she realized that her interest was turning to the intersection of Computer Science and Mathematics. "Nowadays I identify much more as a mathematician than as a computer scientist," she says.

After completing her master's degree in Systems and Computer Engineering, also at UFRJ, in 2014, Taísa was finally able to consolidate her relationship with Mathematics. During her doctoral studies at the University of Warwick, she conducted research in the areas of graph limits and extremal combinatorics.

"At IMPA since 2018, the postdoctoral student considers that IMPA offers an excellent environment for research. The combinatorics research group, in particular, is quite inspiring. In addition to having great national and international visibility, the group is welcoming and friendly. Everyone enjoys discussing, learning about, and developing new problems and techniques," she says.

Taísa already knows what she will do when she finishes her studies at IMPA. She was approved in the competitive examination for a teaching position in the Department of Analysis at the Federal Fluminense University (UFF), and hopes to start working there in 2020.