Abel Prize winner Faltings’ research highlighted at IMPA

The research that led German mathematician Gerd Faltings to the 2026 Abel Prize was at the center of discussions at IMPA in a special lecture given by researcher Hossein Movasati on Tuesday (19). The meeting gave the audience an overview of the contributions that have transformed arithmetic geometry in recent decades, covering topics such as the demonstration of Mordell’s Conjecture, abelian varieties and the influence of the theory of motives on contemporary mathematics.

“IMPA’s mission is to promote mathematics at all levels. Whenever an important prize is announced, we try to give a talk on the subject. It’s an opportunity to learn a little about the mathematics developed by top researchers,” said researcher Luiz Henrique de Figueiredo, organizer of the event.

Hossein Movasati and Luiz Henrique de Figueiredo

Winner of the 2026 Abel Prize for his “fundamental contributions to arithmetic geometry”, Faltings is considered one of the most influential mathematicians of his generation. The lecture at IMPA revisited results that have marked modern number theory and continue to inspire new lines of research around the world.

“This event is an opportunity to learn a little bit about these great mathematicians. Hossein gave a beautiful lecture on the contributions of Gerd Faltings. The importance lies precisely in getting an overview of an area that is not always close to our work,” commented researcher Carolina Araujo.

The presentation began with Faltings’ historic demonstration of the Mordell Conjecture in 1983. The problem stated that algebraic curves of a certain type have only a finite number of rational points, a central issue in modern mathematics. The result earned the German mathematician the Fields Medal and represented a turning point in the field.

Movasati also addressed the development of the arithmetic side of a “heuristic dictionary” proposed by Pierre Deligne in the 1970s, inspired by Alexander Grothendieck’s conjectural theory of motives. The program connects different areas of contemporary mathematics and has influenced topics such as p-adic Hodge theory, period domains and Simpson’s correspondence.

Another highlight was the study of the arithmetic properties of abelian varieties, one of the main focuses of Faltings’ scientific career and a fundamental theme in the interface between algebra, geometry and number theory.

Throughout its history, IMPA has held similar meetings on different awards and researchers who have marked the history of mathematics, including lectures dedicated to Karen Uhlenbeck, Yves Meyer, Andrew Wiles and Maryam Mirzakhani.