Marcelo Campos
Mathematics
Campos, a researcher at IMPA, is deeply engaged with Ramsey graph theory, an enduring and challenging mathematical problem that remains unsolved. To address this problem, he combines elements of randomness and algebra.
Campos’s mathematical journey began early. In high school, he attended seminars at the University of São Paulo (USP) and then began an undergraduate program in applied mathematics there. He then moved on to earn a master’s degree in mathematics at IMPA, followed by a bachelor’s degree at the Federal University of Rio de Janeiro. He returned to IMPA for his doctorate and later undertook postdoctoral research at the University of Cambridge and the University of Oxford.
Outside of mathematical articles and equations, Campos enjoys collecting jokes, stories, and movies. He has a particular fondness for animated films, especially “Puss in Boots 2.”
Projects
The project will investigate the fundamental properties of connection networks, also known as graphs. According to Ramsey theory, specific patterns, such as fully connected or entirely disconnected groups, will inevitably appear in any sufficiently large graph. A central question is: how large can a graph be and still avoid such substructures? In other words, what is the maximum size of a graph that lacks these Ramsey-type patterns? This fundamental problem remains unsolved. Successful approaches to this challenge often involve constructing graphs at random, connecting points by chance, or using algebraic methods, such as solving polynomial equations. My research will pursue a relatively unexplored strategy that combines elements of randomness and algebraic structure to address this longstanding question.
Amount invested
Institutions
- Instituto de Matemática Pura e Aplicada
