Speaker: Jorge Cabral

Title: Data-Driven Support Space Selection for Generalized Cross Entropy Estimation

Abstract: Understanding how multiple factors jointly influence an outcome is central to data analysis, and linear regression remains one of the most powerful and widely used tools for this purpose. The standard method for estimating regression coefficients, Ordinary Least Squares, is unbiased but can become unstable, especially when variables are correlated or data are noisy. Ridge regression addresses this issue by introducing regularization to improve stability. The Generalized Cross Entropy framework provides an alternative perspective, particularly useful when models are ill-specified or data are incomplete. However, its implementation requires specifying discrete support spaces for both the coefficients and the noise—information that is often unavailable in practice. In this talk, we introduce two new methods for selecting these support spaces: one based on the Ridge trace and another on the distribution of standardized coefficients. To facilitate their practical use, we implemented these methods in R, developed the accompanying GCEstim R package, and built an interactive Shiny web application.

Speaker: Luís Castro

Title: On the solutions to a Riemann-Liouville fractional $q$-derivative boundary value problem

Abstract: We will propose a method to obtain conditions that guarantee (several) positive solutions for a class of (nonlinear) $q$-fractional boundary value problems ($0<q<1$), involving the Riemann-Liouville fractional $q$-derivative operator and a $q$-integral condition. A core point of the method is based on a certain combination of convexity arguments along with upper and lower solutions.

The talk will be based primarily on the paper: L. P. Castro, On the solutions to a Riemann-Liouville fractional $q$-derivative boundary value problem, Fractional Calculus and Applied Analysis 28 (2025), 2302–2332.

Speaker: Romain Gervalle

Title: A finite element framework for stationary solutions in curved spacetime

Abstract: We present a new numerical framework for constructing stationary, axially symmetric solutions in curved spacetime and efficiently computing their key physical properties. The code is based on the finite element solver FreeFem, which requires the field equations to be recast in weak (variational) form. We introduce this formalism in the context of gravitational systems, and illustrate its applications to the construction of rotating boson stars and hairy black holes. The code is parallelized to achieve fast and accurate solutions, is publicly available on Git, and can be readily adapted to other systems. We also discuss possible extensions and future developments.

Speaker: Daniel Graça

Title: Analytic maps and Turing universality

Abstract: The iteration of quadratic maps such as the logistic map is well-known to originate complex dynamical behaviour such as chaotic behaviour. In the 1990s Moore asked whether the iteration of analytic maps would be complex enough to not only generate chaotic behaviour, but also to be Turing universal on compact sets, and conjectured that the answer was negative. In this paper we explore this question and related results and show that, under fairly general conditions, the answer to Moore's conjecture is indeed negative.

Speaker: James Kennedy

Title: Spectral and geometric partitions of domains

Abstract: Spectral minimal partitions (SMPs) are a way of dividing a domain into roughly equal pieces in some analytic sense, usually done by minimising some functional of the Dirichlet Laplacian eigenvalues on each element of the partition. They were introduced principally due to their natural ties to the eigenvalues and eigenfunctions of the whole domain; however, their analogues in the discrete setting (for analysing clustering in graphs) can stand in as a substitute for similar geometric functionals. We will give a (very) brief overview of the history and motivation for studying such SMPs, and then present some new results on SMPs based on Robin Laplacian eigenvalues. These make the link to the geometry explicit: we will show that in the degenerate limit as the boundary parameter in the Robin condition tends to zero, the optimal Robin partitions converge to the optimisers of the so-called Cheeger problem, which consists of minimising a functional based on the size of the boundary of the partition elements.

This talk will be partly based on joint projects with Pêdra Andrade, Nuno Carneiro, Matthias Hofmann, João Ribeiro, and Hugo Tavares.

Speaker: Rute Lemos

Title: Elliptical higher rank numerical range

Abstract: The higher rank numerical range of a complex matrix is a compact convex set that generalizes the classical numerical range. This concept was introduced in 2006 by Choi, Kribs and Zyczkowski, motivated by problems in quantum error corrections. We consider these sets for 2-by-2 block matrices with associated Kippenhahn curves consisting of ellipses and eventually points. As a consequence, using a unified approach, elliptical higher rank numerical ranges of tridiagonal matrices are also presented. This is based on a recent joint work with N. Bebiano and G. Soares.

[1] M.-D. Choi, D. W. Kribs, K. Życzkowski, Quantum error correcting codes from the compression formalism, Rep. Math. Phys. 58 (1) (2006), 77-91.

[2] M.-D. Choi, D. W. Kribs, K. Życzkowski, Higher-rank numerical ranges and compression problems, Linear Algebra Appl. 418 (2006), 828–839.

Speaker: Marco Arien Mackaaij

Title: Kostant's problem for fully commutative permutations

Abstract:  Kostant's problem is a well-known problem in the representation theory of complex semi-simple finite-dimensional

Lie algebras, defined and popularized by Joseph in a famous paper from 1980. It asks for which simple modules L of such a Lie algebra g the universal enveloping algebra U(g) surjects onto the space of adjointly finite linear endomorphisms of L. If L is finite-dimensional, the answer follows from the Artin-Wedderburn theorem, but if L is infinite-dimensional, the answer is not known in general. In my talk, I will explain what the answer is for a natural class of simple modules of the special linear Lie algebra sl(n) which are indexed by fully commutative permutations. This is joint work with Volodymyr Mazorchuk and Vanessa Miemietz.

Speaker: Sónia Pais

Title: Learning Mathematics through Play: The Pi Museum Experience

Abstract: In this presentation, I will share the experience of creating and implementing a virtual Educational Escape Room (EER) called Pi Museum, designed to promote interactive mathematics learning within the context of the International Day of Mathematics (14 March), also known as Pi Day. The EER was implemented with 6th-grade classes in a Portuguese school as a formative assessment tool. Its storyline was structured to strengthen students' knowledge of the number π, its history and applications, and to consolidate geometric concepts such as perimeter, area and volume, wherever possible involving π. The experience showed that gamification facilitates knowledge acquisition, increases students´ motivation, and fosters teamwork. Students reported feeling motivated and enthusiastic, describing the experience as both fun and meaningful. Grounded in problem-solving and interactive challenges, this approach not only strengthened mathematical knowledge but also supported the development of transversal skills essential to students’ overall growth.