Monday, July 22nd

Chair: Delfim Torres

15:00-15:10 -  Opening

Systems and Control Group

15:10-15:25 -  Natália Martins

Title: Systems and Control Group: an overview

Abstract: In this presentation, we will outline the main goals of the group and share the latest results obtained by our members.

15:25-15:50 -  Daniel Graça

Title: Computability and dynamical systems

Abstract: In this talk we overview the origins and motivations underlying computability theory. We then survey some applications related to dynamical systems.

History of Mathematics and Mathematical Education Group

15:50-16:05 -  Hélder Pinto

Title: Do passado para novos desafios

Abstract: Desde 2020, o grupo de investigação em História da Matemática e da Educação Matemática dá continuidade ao trabalho do grupo de investigação em História da Matemática, que foi fundado em 2001 como o 7º grupo de investigação do centro de investigação UIMA (Unidade de Investigação em Matemática e Aplicações ). 

A entrada de novos membros nos últimos anos (incluindo um professor visitante de França) permitiu-nos enfrentar novos desafios. Para além da continuação de projetos de investigação individuais, isto inclui, entre outras atividades, o desenvolvimento de um projeto de investigação internacional (a concorrer a uma COST Action) e a organização do ESU-10 em 2026.

16:05-16:30 -  Coffee break

Gravitational Geometry and Dynamics Group

16:30-16:45 -  Carlos Herdeiro

Title: A brief overview of the GDG group and its scientific work

Abstract: I will overview the history of the GGDG within CIDMA and provide some highlights of its scientific work.

16:45-17:10 -  Robertus Potting

Title: Quantum gravity, Lorentz symmetry, and the Standard Model Extension

Abstract: One of the cornerstones of the Standard Model of particle physics and of general relativity is Lorentz symmetry. It was first tested experimentally already in 1887 by Michelson and Morley. Since the 1990's there has been a revival of interest in experimental tests due, in particular, to the fact that some theoretical approaches to quantum gravity can accommodate small deviations from Lorentz symmetry. This talk will start with a brief review of how Lorentz symmetry could be broken in some of these theories. Then it is shown that a natural, systematic way to parametrize small deviations from Lorentz symmetry is by using an effective field theory, the so-called Standard-Model Extension.

17:10-17:35 -  Paulo Sá

Title: Interaction Between Dark Energy and Dark Matter

Abstract: At the end of the 1990s, cosmological observations revealed, not without surprise, that the Universe is presently undergoing a period of accelerated expansion driven by dark energy. A compelling body of evidence also shows the existence of dark matter, another elusive component of the Universe. Despite all observational and experimental efforts, the physical nature of both dark energy and dark matter remains a mystery.

In recent years, I have been studying cosmological models in which dark energy, modeled as an inflaton-like scalar field, and dark energy, represented either by a perfect fluid or by a rapidly oscillating scalar field, interact directly with each other. Using mainly methods of qualitative analysis of dynamical systems, I have investigated the consequences of the interaction between dark components on the Universe's evolution.

In my presentation at the CIDMA-UAlg meeting, I will speak about these so-called coupled quintessence cosmological models, the mathematical methods used to study their evolution, and the main results obtained.

Tuesday, July 23rd

Chair: Daniel Graça

Optimization Graph Theory and Combinatorics Group

09:00-09:15 - Alexander Plakhov

Title: An overview of the OGTC group

Abstract: In the presentation, we will give a short description of main research areas and scientific results of the Optimization, Graph Theory, and Combinatorics group.

Complex and Hypercomplex Analysis Group

09:15-09:30 -  Milton Ferreira

Title: Operator calculus on Spin(4) 

Abstract: In this talk, we present a full symbol calculus of pseudo-differential operators on the group Spin(4). The essential tools for such calculus are the Spin(4)-representations, its matrix coefficients, recurrence relations, difference operators acting on them, and the Fourier transform on Spin(4). Spin(4)-representations are constructed in the spaces of simplicial harmonic and spinor-valued monogenic polynomials using Clifford analysis tools. We characterize elliptic and global hypoelliptic pseudo-differential operators in Spin(4), in terms of their matrix-valued full symbols. Some examples will be given. 

Algebra and Geometry Group

09:30-09:45 -  Dirk Hofmann

Title: Presentation of the Algebra and Geometry Group 

Abstract: After a brief presentation of the group, in this talk we give a short introduction into our work on (the double category of) coalgebras, in particular on the existence of the final coalgebra and on behavioral equivalence. 

09:45-10:10 -  Marco Mackaay

Title: Categorification

Abstract: The term “Categorification” was introduced by Louis Crane in 1994 and the idea originates in his joint work with Igor Frenkel on canonical bases and four-dimension topological quantum field theories. Roughly speaking, it refers to the process of replacing certain set-theoretic notions by analogous categorical notions, e.g. algebras by monoidal categories and polynomial invariants in low-dimensional topology by graded homologies. In my talk, I will briefly explain what categorification is about and sketch some of the most remarkable examples of categorification and their consequences.

10:10-10:35 -  Diana Rodelo

Title: The matrix trick - how to translate varietal proofs into categorical ones

Abstract: While studying algebraic categories we find many definitions of categories that were adapted from known notions in the context of varieties of universal algebras. For example: Maltsev categories are the categorical translation of Mal'tsev varieties and unital categories correspond to Jónsson-Tarski varieties. These varietal notions, well known in Universal Algebra, may be characterised in a simple way through the existence of certain operations and identities between them. Then, using the elements of the algebras and the operations and identities on them usually leads to nice simple proofs. When dealing with the corresponding categorical context we cannot use elements nor the operations applied to them, so these handy tools are lost (or not?). The following question naturally arises: Is it possible to translate a (simple) varietal proof which uses operations and its identities into a categorical proof? The goal of this talk is to explain a recent approach, called here the matrix trick, that provides a positive answer to this question. This approach is based on a matrix representation of the operations and identities which characterise a variety and its corresponding equivalent properties involving relations.

10:35-11:00 -  Coffee break

Functional Analysis and Applications Group

11:00-11:25 -  Ana Conceição

Title: The use of symbolic computation in operator theory algorithms

Abstract: Since the beginning of my research activity in the area of ​​operator theory, I have dedicated part of my time to the design of analytical algorithms for solving certain problems related to the resolution of singular integral equations, factorization of matrix functions and the study of the spectrum and the kernel of some classes of singular integral operators. After completing my PhD, I started using the symbolic computation capabilities of the Mathematica computer algebra system to implement particular cases of the algorithms on a computer. It has been an interesting experience, however, sometimes frustrating in terms of choosing journals for publication, due to the multidisciplinary nature of some of the results (that complicates the process) and the lack of similar algorithms for the same types of problems. This line of research demands a solid grasp of operator theory concepts and an understanding of what is achievable through symbolic computation.  Additionally, I have to have someone I trust for programming tasks. In our meeting, I look forward to sharing more about my experiences in this exciting field.

Probability and Statistics Group

11:25-11:40 -  Adelaide Freitas

Title: Presentation by the Probability and Statistics group

Abstract: An general description of the CIDMA's Probability and Statistics group is presented, giving a brief description of some of the group's main research areas.

11:40-12:05 -  Clara Cordeiro

Title: Resampling Revelations

Abstract: In recent years, resampling techniques for dependent data have been applied in several time series approaches as a way of reducing uncertainty, such as in forecasts. Nonetheless, is it worth employing these techniques? In this meeting, I will present an overview of my research, illustrated by some case studies.