Algebra and Geometry Group

Ariel Martín Pacetti
Title: A simplified proof of Serre's conjectures.

Abstract: in this talk we will explain a series of conjectures made by Serre in the mid seventies and proven in 2005 by Khare and Wintenberger. We will give a sketch of a simplified proof of it (using modern results unavailable at the time).

Rui Prezado

Title: Local-to-global principles

Abstract: Local-to-global principles are ubiquitous in mathematics, particularly in algebra and geometry. Grothendieck's descent theory, and subsequent generalizations, employ a categorical approach to provide tools for the study of local-to-global princples, which has found several applications to the Galois theory of various settings. We will discuss the basic ideas behind this categorical development of descent theory.

Complex and Hipercomplex Analysis Group

Helder Lima

Title: Hypergeometric multiple orthogonal polynomials

Abstract: The central topic of this talk (and of my research) are multiple orthogonal polynomials, a generalisation of classical orthogonal polynomials satisfying orthogonality conditions with respect to systems of several measures rather than just one measure. I will present a family of multiple orthogonal polynomials which admit explicit representations as terminating hypergeometric series and are connected to several fields of Mathematics.

Uwe Kaehler

Title: Grothendieck-Lidskii trace formulae in case of spinor-valued functions

Abstract: In 1955 Grothendieck constructed trace formula for topological tensor products in the case of locally convex spaces over commutative structures. Many attempts have been made to extend this result to noncommutative structures, such as by F. Trèves and E. Stein. The most recent results were obtained by M. Ruzhansky in the case of nilpotent Lie groups. Unfortunately, the important case of Spin groups does not fall under the previous case since Spin group have only a periodic and not a nilpotent behavior. Here, we are showing how one can combine techniques by Gelfand with our own methods to establish a Grothendieck-Lidskii trace formulae in the case of locally convex function spaces over spinor-valued functions.

Functional Analysis and Applications Group

Alexandre Almeida

Title: Variable Exponent Besov–Morrey Spaces

Abstract: We introduce a new scale of non-standard function spaces from a quite general abstract setting. This scale includes, as particular cases, various function spaces studied separately in the literature.

Some key properties, such as maximal functions characterization and atomic decompositions are obtained.

This work required the development of new tools, namely a special convolution inequality which proved to play a crucial role.

This is based on joint work with António Caetano. 

Ana Conceição
Title: Computation Applied to Function Factorization Concepts: the Rational Scalar Case
Abstract: Factorization theory finds extensive applications in various fields, including the theory of non-linear and linear differential equations, theory of diffraction of acoustic and electromagnetic waves, scattering theory, among others. While significant progress has been made for certain classes of functions that permit specific strategies for factorization, there is no general method for obtaining a factorization for a given function. In our research, we design and implement operator theory algorithms. Using the numeric and symbolic computation capabilities of the Wolfram Mathematica computer algebra system, we create new tools that simplify complex and lengthy calculations for researchers across different areas. In this talk we present new rational factorization algorithms that enhance the design and improvement of other operator theory algorithms. 

Gravitational Geometry and Dynamics Group

Carlos Herdeiro

Title: Light ring topological theorems: shedding light on the dark side
Abstract: After a short overview of the work of GGDG group, I will focus on a line of scientific work, proposed by the group, on theory independent spacetime properties. This set of results determine the existence and properties of special geodesics, called light rings, around compact objects in arbitrary theories of gravity, being established by a set of topological theorems. I will then explain on how this can impact on our knowledge of compact objects in the universe in a dramatic way.

Raimon Luna

Title: Application of machine learning to strong gravity

Abstract: Machine learning is quickly becoming a state-of-the-art tool for fundamental scientific research in gravity. This tool has the potential to greatly reduce the computational cost of numerically solving problems in general relativity, and promises to improve our ability to quickly model strong gravitational systems. This talk will focus on the use of machine learning techniques as a research tool in strong gravity.

History of mathematics and Mathematical Education Group

Ana Patrícia Martins

Title: Topics on the history of the inclusion–exclusion principle

Abstract: In this presentation I will contextualize my research activity in the History of Mathematics, which has a greater focus in the History of Actuarial Calculus. Particularly, I will present one of my published contributions, an analysis on the formulations of the inclusion–exclusion principle from Legendre to Poincaré, with emphasis on Daniel Augusto da Silva. Da Silva is one of the most relevant Portuguese mathematicians of the 19th century and that topic is mentioned in a major work which gives him the priority on methods of solving systems of linear congruences.

Helmuth Malonek 
Title: The year 2024 - in view of new horizons

Optimization, Graph Theory and Combinatorics Group

Alexander Plakhov
Title: Newton’s least resistance problem for convex bodies
Abstract: I. Newton in 1687 posed the problem of optimal streamline shape for rotationally symmetric bodies moving in a rarefied medium and indicated its solution. Buttazzo and Kawohl (1993) extended the problem to the wider class of convex (not necessarily symmetric) bodies. The problem in this setting is not solved in full until now. We report solution of three related conjectures stated nearly 30 years ago.
1) An optimal function (describing the front part of the body surface) vanishes on the boundary of its domain.
2) The slope of the surface of an optimal body near its front part is 45º.
3) The surface of an optimal body outside its singular set is foliated by line segments.

Probability and Statistics Group

Pedro Macedo

Title: Some maximum entropy methodologies in the study of climate change 

Abstract: The maximum entropy bootstrap for time series, by not imposing parametric restrictions, allows greater freedom in statistical modeling and inference. A recent proposal to improve the estimation of parameters through generalized maximum entropy will be discussed and illustrated in studies of climate change.   

Marco Silva

Title: Quality 4.0 in an automotive company: integration of Computer Vision and Machine Learning – Challenges 

Abstract: In general, technological development applied to solving real-world problems has always been one of my areas of interest. I had the opportunity to do both a summer internship and a curricular internship at Toyota Caetano Portugal S.A., where I established valuable professional connections. These experiences allowed me to develop skills in Quality 4.0 and programming, which later supported my master’s thesis focused on process digitization, particularly through tools for defect recording and monitoring via data analysis.

I started a PhD in Industrial Engineering and Management with the financial support of the Portuguese Foundation for Science and Technology (FCT), conducted in a non-academic environment. The project involves implementing Computer Vision integrated with Machine Learning to detect and analyze data in Toyota Caetano Portugal S.A. It aims to solve quality issues in the logistics supply process by recognizing different parts that compose the dollies supplying the production line. The system is expected to identify incorrect parts, categorize this information, and generate real-time reports with trend analysis supported by Machine Learning. Additionally, it should enhance the supply process and improve working conditions for operators. The tool aims to support operational improvements and decision-making for managers. From a scientific perspective, integrating these tools will explore their potential in industrial contexts and broaden their applicability to other sectors. The main goal of the project is divided into two. From a research standpoint, it aims to understand how two AI categories—Computer Vision and Machine Learning—can be integrated, particularly in an industrial context, and their impact on Quality 4.0. From an applied perspective, the aim is to address a real-world quality assurance problem in the logistics supply process. This involves specifying, developing, and implementing an original and efficient system for detecting incorrect or damaged parts and transmitting this information to the operator in real time, followed by data analysis via Machine Learning to support managerial decision-making. Additionally, alongside contributing to the company’s technological development, the project considers human factors by improving operators’ working conditions and promoting sustainability through waste reduction and process efficiency. The development, implementation, and refinement of this system aims to serve as a benchmark for other companies facing similar challenges, thereby actively contributing to organizational performance improvement, waste reduction, and sustainability.   

Systems and Control Group

Carla Pinto

Title: To Be or Not To Be Fractionalizers Mathematical Epidemiologists

Abstract: We explore key challenges in accurately deriving epidemiological compartmental models. Recently, fractional-order models have proliferated, often developed by generalizing integer-order to fractional-order derivatives. This ad hoc approach may compromise physical validity and mass conservation. We advocate for probabilistic methods, like survival functions, to ensure sound physical interpretation.  

Raquel Pinto

Title: State-space realizations of periodic convolutional codes

Abstract: In this talk we present state space representations of periodic convolutional codes. These representations can be implemented by realizing two linear time-invariant systems separately and switching the output that is leaving the system. We also investigate their minimality and provide necessary and also sufficient conditions in terms of the reachability and observability properties of the two linear systems involved.