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October 24th, 2025
09h30 - 09h45 Welcoming & Opening Session
09h45 - 10h45 Zita Abreu (Former student) - Constructing New Families of Optimal Convolutional Codes over Small Finite Fields
10h45 - 11h15 Coffee-Break
11h15 - 11h45 Márcia Lemos - A consistent SIR model on time scales with exact solution
11h45 - 12h15 José Ferreira - Black Holes as Particle Accelerators
12h15 -12h45 Beatriz Teixeira - A Brief Introduction to Category Theory and Duality
Chairs: Juliana Cunha
Zita Abreu
Title: Constructing New Families of Optimal Convolutional Codes over Small Finite Fields
Abstract: In this talk, we focus on the challenging task of constructing new families of optimal convolutional codes over the smallest possible finite fields. Specifically, we explore the construction of maximum distance separable (MDS) and maximum distance profile (MDP) convolutional codes using different construction strategies. Since efficient decoding is also a key concern, we present a decoding algorithm tailored for a specific class of optimal binary convolutional codes that we construct. Our results demonstrate that these code constructions and decoding techniques provide a novel and comprehensive perspective on convolutional codes.
Márcia Lemos
Title: A consistent SIR model on time scales with exact solution
Abstract: We propose a new dynamic SIR model that, in contrast with the available model on time scales, is biological relevant. For the new SIR model we obtain an explicit solution, we prove the asymptotic stability of the extinction and disease-free equilibria, and deduce some necessary conditions for the monotonic behavior of the infected population. The new results are illustrated with several examples in the discrete, continuous, and quantum settings.
José Ferreira
Title: Black Holes as Particle Accelerators
Abstract: Advances in modern observatories have transformed black holes from purely theoretical constructs into observable astrophysical objects. Surprisingly, black holes can interact with their surroundings without destroying them. One such interaction arises through superradiance, a process in which particles extract energy from a black hole. Under the right conditions, these particles can stabilize around the black hole, giving rise to so-called hairy black holes. The detection of such objects would provide indirect evidence for the existence of new particles. This raises a fundamental question: are hairy black holes dynamically stable and can we detect them?
Beatriz Teixeira
Title: A Brief Introduction to Category Theory and Duality
Abstract: Category Theory is a relatively new area of mathematics that, in the words of Leinster, "takes a bird's eye view" of all of mathematics as it provides a way of spotting patterns between different areas. Not as superficially, it encourages a shift in what one classifies as a structure, as most times it does not care about the inner workings of the objects themselves but how they correlate to each other, via morphisms, in the category they sit in. In this talk we give a very brief introduction to category theory and one of its many branches, duality theory. We pay special attention to the Lindenbaum-Tarski Duality (1935) which states that the dual category of sets is equivalent to the category of complete atomic boolean algebras (CABA). If time permits, we will go a step further and see some more examples of known dualities.
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