Igor Soares talks to students about Percolation and Critical Exponents

At the invitation of the graduating class of 2025, IMPA doctoral student Igor Soares gave a seminar on “Percolation and Critical Exponents” on Tuesday (9) at IMPA Tech. The presentation brought an interdisciplinary approach between mathematics, physics and computer science with practical applications.

Soares gave an introduction to the Percolation model, discussing both classical results and problems that are still open in the area. The event also covered the concept of Critical Exponents – fundamental to understanding phase transitions in disordered systems. The speaker also explored the computational methods used to estimate these exponents, a central theme of his current research at IMPA.

“Percolation is a classical branch of probability, which is linked to particle systems. It’s motivated by physics and has various problems, such as: ‘Is there an infinite random subgraph? This is the kind of question that percolation is concerned with. My work is linked to this, but also to simulations of these models. It’s work that brings together both areas, mathematics and computer science,” he explained.

The aim of the lecture was to provide an accessible overview that connects mathematical theory with its practical applications, as well as presenting the modern simulation techniques that are being developed in the field.

“My expectation today is to make a simple presentation to introduce this subject, which is new, to the students. I don’t want it to be complicated or too technical. The idea is to show the models we study, what kind of question we’re interested in answering, giving a glimpse of the mathematics behind it,” he said.

The presentation of the topic aroused the students’ curiosity. Emilly Rezende intends to continue her research into the subject after the lecture. “I really liked the topic, I’d never heard of it and I realized that there are several applications, including in physics, which is an area that interests me a lot. I’m certainly going to do more research on the subject.”

The didactic way in which Igor conducted the seminar was also praised by the participants. Matheus Galvão highlighted the interactivity as a highlight. “I thought it was great that he made room for questions during the presentation. That way we don’t get lost and everything is less confusing.” Ruan Martins valued the connections with concrete examples. “The applications he brought helped a lot in understanding the topic.”

 

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