News and Events

Get ready for Náboj 2026, the international mathematics competition whose Portuguese edition will be hosted by Instituto Superior Técnico. In this fast-paced contest, teams from five secondary schools race against the clock to solve as many problems as possible in 120 minutes. Unlike standard school exercises, Náboj problems are designed to challenge ingenuity and logical thinking, making the competition exciting for both newcomers and experienced olympiad participants. Teams compete in Junior (up to 10th grade) and Senior categories, with the chance to compare results internationally against students from over a dozen countries. Registration is now open, so gather your team, put your problem-solving skills to the test, and discover the infinite beauty hidden in mathematics!

The next edition of GEMS (GEometry MeetingS) is coming soon. This is a collaborative initiative supported by five Portuguese research centers aimed at strengthening the geometry research community. The meeting will feature topics ranging from the topology of higher-dimensional automata to critical metrics and primitive immersions. These regular gatherings provide an informal and engaging environment for researchers to exchange ideas and explore emerging trends in geometry and related areas. For any information, please feel free to contact the organizers.

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

In the special session of the Explica-me como se tivesse 5 anos series our colleague Hugo Tavares (CAMGSD/Department of Mathematics) will lecture on a fun and fascinating question: Why are soap bubbles round?.

This talk is aimed at curious minds of all ages, especially younger ones. Through playful experiments with soap films, Hugo will show how geometric forms like circles and hexagons are often the best solution for some beautiful geometric problems from the natural world, from bubbles to beehives. Don''''''''t miss this chance to see the beauty of mathematics in action and discover why some shapes are perfectly suited for what they do. All are welcome!

The Shape Optimization & Spectral Minimal Partitions workshop is an international meeting that will bring together leading experts and young researchers to explore the latest developments at the intersection of shape optimization and the theory of spectral minimal partitions. The program features a distinguished lineup of plenary speakers, alongside a session for short communications. Participation is free of charge; those interested in attending are invited to register by contacting organizer Hugo Tavares directly. We look forward to fostering rich discussions and collaborations in the beautiful setting of Aveiro.

Lorentzian Geometry provides the mathematical foundation for Einstein’s theory of Relativity. The Meeting is aimed to convey researches on all aspects of Lorentzian Geometry. Topics include Differential Geometry, Geometric Analysis, Partial Differential Equations and Mathematical Relativity. The Meeting comprises research talks, a mini-course and a poster session, as well as a social dinner. Students and young researchers are encouraged to participate

This workshop brings together leading researchers working on stochastic processes, interacting particle systems, and their wide-ranging applications in mathematics, physics, and beyond. Organized as part of the LiBERA midterm workshop under the Horizon Europe Marie Skłodowska-Curie Actions Staff Exchanges (project no. 101183168LiBERA), it offers a unique opportunity for cross-disciplinary exchange at the interface of analysis, probability, mathematical physics, numerics and applications.

The program features 26 talks showcasing the latest results and innovative applications, providing a platform for lively discussions and knowledge sharing.

• Deadline for submission of contributions: 28 February 2026.
• Registration: free of charge, but mandatory by 31 March 2026.

Local organizers: Gerardo Barrera Vargas, Patrícia Gonçalves and Tiecheng Xu.

A breakthrough in mathematical physics resolved a major open problem by rigorously deriving the Boltzmann equation from the dynamics of individual atoms

In a landmark paper, Long time derivation of the Boltzmann equation from hard sphere dynamics, mathematicians Yu Deng, Zaher Hani, and Xiao Ma rigorously derived the Boltzmann equation describing the behavior of a gas at the mesoscopic scale, directly from Newton''''''''s laws applied to individual spherical (hard) atoms. This work extends a 1975 theorem by Oscar Lanford, which proved such a connection for short-time. 

A recent article from Quanta Magazine article straightforwardly describes this achievement. A key idea consists in using techniques from the study of wave interactions to create a "cutting algorithm" managing the complexity of possible collision histories among particles. This is then used to prove that complicated, recurring collisions are extraordinarily rare. This work appears to give insight into the problem of understanding how the arrow of time seen at the macroscopic scale emerges from time-reversible laws ruling the microscopic world. This result, together with previous work, solves an aspect of Hilbert''''''''s Sixth Problem.

O Professor António Ferreira dos Santos nasceu em Almeirim, em 1939, e dedicou a sua vida académica ao Instituto Superior Técnico, em particular ao Departamento de Matemática. Dotado de uma notável capacidade de coordenação e liderança, colocou a sua criatividade e visão científica ao serviço da investigação desenvolvida no Departamento de Matemática.

Distinguindo-se como o melhor aluno do Liceu de Santarém em 1957, António Ferreira dos Santos obteve uma bolsa da Fundação Calouste Gulbenkian, que lhe permitiu concluir a licenciatura em Engenharia Eletrotécnica no Instituto Superior Técnico, em 1963. Em 1966, novamente com o apoio da Fundação Gulbenkian, deslocou-se para Londres, onde obteve o grau de Doutor em Engenharia Eletrotécnica pelo Imperial College, com um trabalho na área da propagação de ondas. No final da década de 80, decidiu centrar a sua atividade científica na área da Matemática. Em 1989 obteve a Agregação em Matemática. Desde então, exerceu funções como Professor Catedrático no Departamento de Matemática.

O Professor Ferreira dos Santos desempenhou diversos cargos de elevada responsabilidade académica, tendo sido Presidente do Instituto Superior Técnico entre 1978 e 1979, Presidente do Conselho Pedagógico do Instituto Superior Técnico entre 1979 e 1980, Presidente do Departamento de Matemática nos períodos de 1983 a 1984 e de 1991 a 1992, bem como Presidente do Conselho Científico do Instituto Superior Técnico nos mandatos de 2001 a 2002 e de 2003 a 2004.

Foi ainda membro de várias estruturas de gestão e coordenação do Departamento de Matemática. Esteve na criação do Mestrado em Matemática Aplicada, do qual foi coordenador entre 1983 e 1991, tendo lecionado diversas unidades curriculares, nomeadamente Análise Funcional, Análise Complexa, Operadores Lineares e Operadores Integrais.

Foi o principal fundador do Centro de Matemática Aplicada, posteriormente Centro de Matemática e Aplicações, bem como do Centro de Análise Funcional e Aplicações, do qual foi presidente até à sua jubilação, em 2009.

Criou um grupo de investigação em Teoria de Operadores, integrando-o na comunidade científica internacional. A sua investigação contribuiu de forma significativa para o desenvolvimento da teoria da fatorização e da teoria dos operadores integrais singulares, destacando-se, em particular, os seus contributos para a fatorização de funções matriciais do tipo Daniele–Khrapkov e para a fatorização em superfícies de Riemann, bem como para a análise de Fredholm de equações em intervalos compactos. Salientam-se ainda os seus trabalhos na aplicação da teoria da fatorização a sistemas integráveis e à teoria da difração de ondas. Publicou cerca de meia centena de artigos científicos e orientou várias teses de doutoramento.

O Professor Ferreira dos Santos, pela sua determinação e paixão pelo conhecimento, deu contributos de elevado nível para o desenvolvimento da investigação científica em Portugal. Para todos quantos com ele contactaram, será sempre uma referência de rigor académico, espírito democrático na relação entre colegas e permanente procura da excelência científica.

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

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. 

We are delighted to announce that Francisco Cunha, an alumnus of the Bachelor’s in Applied Mathematics and Computation (LMAC), will present a paper at the AAAI 2026 conference, one of the world’s leading artificial intelligence events. The presentation, titled Generalizing Analogical Inference from Boolean to Continuous Domains, will be part of the Knowledge Representation & Reasoning (KRR) track. This notable research was conducted in collaboration with, among others, Professor Miguel Couceiro from our Mathematics Department. Francisco, currently pursuing a master’s degree at the University of Oxford, and his co-authors propose a unified framework that generalizes analogical inference to continuous domains, overcoming limitations of previous models and opening new avenues for applications in regression and machine learning tasks. It is an honor to see the brilliance of our former students recognized on the most prominent stages of international research.

Three students from the Applied Mathematics and Computation (MAC) programme are among the eleven from Instituto Superior Técnico awarded the Gulbenkian Novos Talentos scholarships for 2025. This program, funded by the Calouste Gulbenkian Foundation, aims to support promising young talent to help them excel in their academic journeys. This achievement recognizes our students’ strong potential and commitment to mathematics.

These students will receive a valuable opportunity to engage in research projects under the supervision of our faculty. We extend our sincere congratulations to the winners and wish them every success as they continue to develop their skills and contribute to the future of applied mathematics and computation.

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.