News and Events

A meeting to discuss recent developments at the interface of geometric topology and homotopy theory.

João Ribeiro received a Starting Grant from the European Research Council (ERC) worth approximately €1.5 million to develop new techniques for studying channels with loss of synchronization—a particular case of communication errors where, for example, some digits may be dropped from the final message, making it difficult to compare with the initial message. Loss of synchronization errors appear in cutting-edge data storage systems, particularly in DNA data storage systems, a promising solution due to their high density and durability.

The Department of Mathematics was featured on CNN Innovation, a television program dedicated to technology and scientific innovation.

Hugo Tavares, vice-president of the Mathematics Department, tells us about Math@Técnico.

Hugo Duminil-Copin is a French mathematician renowned for his outstanding contributions to probability theory and statistical physics, who was awarded a Fields Medal in 2022.

More information including available videos.

Video interview of Diogo Oliveira e Silva and other organizers about the Intensive Research Programme on Modern Trends in Fourier Analysis at CRM, Barcelona. This program focuses on recent developments in Harmonic Analysis, Geometric Measure Theory, and Constructive Approximation, with an emphasis on Fourier uncertainty principles, restriction estimates in Fourier analysis, and analysis in discrete geometry. The aim is to create an ideal atmosphere for significant progress in these areas. To achieve this, leading scientists with expertise in Fourier analysis will bring together their diverse backgrounds, interact, and collaborate to stimulate the development of research. In addition to the Conference and Advanced Courses, there will be regular activities such as weekly seminars and group research sessions.

Hong Wang and Joshua Zahl have solved the three-dimensional Kakeya conjecture, a fundamental problem in geometry that has been open for many decades. The conjecture asks whether the space used to rotate a needle in all directions necessarily has full Hausdorff dimension. Their proof has settled this question positively in dimension three and confirmed deep ties to harmonic analysis.

First posed almost a century ago, the problem rapidly gained prominence through its linkage to other areas of mathematics. Experts hail the work as transformative, potentially unlocking progress on higher-dimensional versions and related open problems. “It’s a once-in-a-century result,” said Nets Katz of Rice University. 

A team of mathematicians has achieved a major breakthrough by proving the geometric Langlands conjecture, a key part of the Langlands programme often called the "grand unified theory of mathematics." Led by Dennis Gaitsgory and Sam Raskin, the proof spans five papers and nearly 1,000 pages, and confirms deep connections between number theory, geometry, and harmonic analysis. The work, earned Gaitsgory the $3-million Breakthrough Prize.

The conjecture, first proposed in the 1980s, links algebraic geometry to representation theory through the study of Riemann surfaces. Beyond its mathematical significance, the geometric Langlands conjecture has surprising ties to physics, particularly to S-duality in gauge theories. 

José Natário and Filipe Mena, both Professors in the Mathematics Department, have been recognized by the University of Lisbon/Caixa Geral de Depósitos Scientific Awards. José Natário was awarded the prize, while Filipe Mena received an honorable mention. These annual awards celebrate outstanding scientific research and encourage publication in high-impact international journals. Congratulations to both for this well-deserved recognition!

The monograph Quasiconformal Mappings in the Plane and Complex Dynamics published by Springer and written by Luis T. Magalhães, Professor in the Mathematics Department, provides an accessible and self-contained introduction to quasiconformal mappings with applications in complex dynamics. It features examples, historical context, and serves as a sequel to the author''''''''''''''''''''''''''''''''s Complex Analysis and Dynamics in One Variable with Applications. 

After a two-year break, Ponto Fixo, the beloved mathematics journal, is back with its fifth edition. Editor Diana Gaspar highlights that while most news would lose relevance over such a gap, mathematics remains timeless, making this edition as valuable today as it would have been in 2023. The latest issue features articles on three of the four 2022 Fields Medal winners, student contributions, and a film review. It also includes interviews with former students discussing whether to pursue a doctorate, reflecting on how advanced degrees are becoming increasingly essential beyond academia.

The journal celebrates tradition and innovation, aligning with NMATH’s newer initiatives like Time2Talk and Integration Bee. Gaspar emphasizes Ponto Fixo’s role in fostering mathematical dialogue, giving students and professors a voice, and rekindling the passion that draws people to mathematics. While aimed at math enthusiasts, the journal welcomes all curious minds, whether they’re solving puzzles, skimming, or reading cover to cover. The editor concludes by thanking contributors and reaffirming the enduring spirit of knowledge-sharing that keeps the journal alive.