Poisson brackets are a central notion in a variety of topics related to mathematical-physics. In this note, we provide an overview of geometric and Lie theoretic aspects behind Poisson brackets and mention some recent ramifications and applications. In particular, we describe the notion of symplectic groupoids viewed as integrations of Poisson manifolds, explicit constructions of these integrations, the general theory of multiplicative structures on Lie groupoids, and applications to quantization and geometric numerical methods.

93rd edition of the Séminaire Lotharingien de Combinatoire (SLC 93)

Interview with the 2025 Pedro Nunes Lecturer, Michael Christ

Nonlinear PDEs in Guimarães

Deep Neural Networks (DNNs) are the main concept at the center of the artificial intelligence revolution we are experiencing. However, some of the reasons behind their effectiveness (for instance, why do they seem to provide ``good’’ solutions, determined by simple optimization algorithms?), as well as the causes of their limitations (for instance, why are they so parameter and data expensive?), remain somewhat unclear. Therefore, a theoretical/mathematical clarification of these issues would be welcomed and, in principle, might help us in the construction of a new generation of interpretable, safer, sustainable and, consequently, more reliable AI models.

With that in mind, a mathematical approach that has provided some relevant insights is the study of the asymptotic structure of DNNs.

In this article, we will start by introducing the basics of DNNs, followed by a presentation of some results concerning the study of the large width limit of these models and a discussion of the implications that such results have in our understanding of supervised machine learning with DNNs.

Report for the conference Interaction of Poisson Geometry, Lie Theory and Symmetry

Report for the 4th Women in Mathematics Meeting in Portugal

Going hyperbolic
 

Report on the 9th edition of the workshop series NTQO—New Trends in Quaternions and Octonions

Report on the 4th Number Theory Portuguese Meeting

Report on the 15th Combinatorics Days

An interview with Hugo Duminil-Copin

Report on the 21st Computability in Europe Conference

Report on the conference XVI Non-Associative Day in Azores

Report on the conference WODCA 2025

Report on the conference Summer JIM Days

The competition Symmetries of Lisbon’s calçada on π Day in 2025

The National Seminar on the History of Mathematics: Thirty eight years of research and dissemination in the History of Mathematics.

Report on the Second Atlantic Conference in
Nonlinear PDEs