A crucial task  in control applications is the design of a feedback operator allowing us to compute a control input which is able to stabilize a given dynamical system, being able to respond to small perturbations as well. Feedback inputs are given as a function of the state of the system, which is often not fully available in real world applications. Thus, another crucial task is the design of a dynamic Luenberger observer providing us with an estimate for the unknown state, by using the output of sensor measurements; here, the task is to find an operator that injects the output into the dynamics of the observer. In this talk, we discuss recent developments on the design of such feedback-input  and output-injection operators for models given by parabolic-like equations. The focus is put on the design of simple and explicit operators. Both theoretical and numerical aspects are discussed, including a comparison to more classical operators obtained through optimal control tools and involving the solution of Riccati or Hamilton-Jacobi-Bellman equations.

Room: 202 ed IV 
 
Abstract: Vectorial Boolean functions are used in cryptography, in particular in block ciphers. An important condition on these functions is a high resistance to the differential and linear cryptanalyses, which are the main mathematical attacks on block ciphers. The functions which possess the best resistance to the differential attack are called almost perfect nonlinear (APN). Almost bent (AB) functions are those mappings which oppose an optimum resistance to both linear and differential attacks. APN and AB functions are important not only for the purpose of constructing new block ciphers in cryptography, but for other areas of computer science and discrete mathematics (such as combinatorics, sequence design, coding theory, design theory) in which APN functions correspond to some optimal objects. In this talk we address some longstanding problems related to APN and AB monomials.

We investigate an eigenvalue problem involving the 1-Laplacian operator on bounded domains with Neumann boundary conditions. The problem is not well posed in standard Sobolev spaces and must be studied in the space of functions of bounded variation, using tools from nonsmooth analysis. We give a geometrical characterization of this eigenvalue in terms of a relative isoperimetric problem. This connection allows us to characterize eigenfunctions in several relevant situations, including C^2 strictly convex domains, and to highlight both uniqueness and symmetry phenomena.

Abstract

Two-stage distributionally robustoptimization (DRO) is a recent optimization technique for handling uncertainty.It is less conservative than robust optimization and more flexible thanstochastic programming. In DRO, the probability distribution of uncertainparameters is assumed to be unknown but to belong to a prescribed ambiguityset. The size of the ambiguity set is frequently governed by a single parameterthat controls the level of conservatism of the resulting optimization problem.Determining appropriate values for this parameter is therefore a key researchchallenge. In this talk, we first introduce a DRO model for the berthallocation problem with uncertain handling times, which is one of the most importantproblems in port terminals. Then, we present methods for identifying suitablevalues of the ambiguity-set control parameter used in the DRO model. Thosevalues are expected to enable us to obtain all relevant first-stage solutionsworth considering.

Abstract: In this talk I will give an overview of what is known about conjugacy growth and the formal series associated with it in infinite discrete groups. I will highlight how the rationality (or rather lack thereof) of these series is connected to both the algebraic and the geometric nature of groups such as (relatively) hyperbolic or nilpotent, and how tools from analytic combinatorics can be employed in this context. I will also mention results about the languages of conjugacy representatives in various groups.

Title: Self-Organized Spreading Dynamics near Criticality
Speaker: Viola Priesmann, Max Planck Institute for Dynamics and Self-Organization
& Georg-August-University Göttingen.

Date | Time: March 20, 2026 | from 14:00 to 14:50.

Place: Room 3 - Building Hangar II.

Abstract: Many living systems, from virus spread in societies to information spread in neural networks, are characterized by stochastic spreading of discrete events on complex networks. This spread then does not occur on a static network, but on an adaptive one, where the spreading proper influences the network’s coupling strength. This feedback loop between spreading activity and coupling strength can generate either stabilize and optimize information flow, or it can generate catastrophic resonance effects. We will investigate how these different phases emerge, and how they shape disease spread and information flow in complex networks.

##################################################################

Title: Near-Threshold Stochastic Dynamics and Arbovirus Emergence in Non-Endemic Regions.

Speaker: Maíra Aguiar, Basque Center for Applied Mathematics (BCAM).

Date | Time: March 20, 2026 | from 14:50 to 15:40.

Place: Room 3 - Building Hangar II.

Abstract: Arboviruses such as dengue and chikungunya are increasingly reported in temperate and non-endemic regions, driven by climate variability, global mobility, and the expansion of competent mosquito vectors. Most risk assessments, however, rely on deterministic metrics like the basic reproduction number (R₀), assuming sustained transmission is unlikely when R₀ < 1. Under this framework, areas with low mosquito abundance, short transmission windows, and sporadic viral importation are considered low-risk.

We show that this approach can underestimate outbreak potential. Many non-endemic settings operate near the transmission threshold, where stochastic effects dominate and rare introductions can trigger substantial outbreaks despite subcritical average conditions. Using the 2024 dengue outbreak in Fano, Italy, we demonstrate that stochastic transmission models reproduce observed outbreak timing and magnitude, whereas deterministic models predict rapid extinction.
This mechanism extends beyond specific case studies: near-threshold stochasticity can generate outbreak patterns resembling supercritical dynamics wherever competent vectors and episodic viral introductions occur. Recognizing these dynamics is crucial for improving epidemic intelligence and public health preparedness. Integrating stochastic models with high-resolution mosquito surveillance, climate data, and human mobility enables more realistic outbreak risk assessments, informing early warning systems and targeted interventions in emerging epidemic settings.

In this talk, I will present a new formulation of the Korteweg-de Vries equation (KdV) on the real line, via a gauge transform. While KdV and the gauged equation are equivalent for smooth solutions, the latter is better-behaved for initial data at lower regularities. In particular, the admissible regularities go beyond the $H^{-1}$-scale, which is a well-known threshold for KdV. As a byproduct, by reversing the gauge transform, we are able to improve on the theory for KdV. Additionally, our method is totally independent of the KdV complete integrability structure, and extends to other non-integrable models with quadratic nonlinearities. 
I will focus mainly on the derivation of the gauged equation: using tree graphs and some basic combinatorics, we will uncover a hidden structure which then gives rise to the announced gauge transform. This is joint work with Andreia Chapouto (CNRS, Monash University, Australia) and João Pedro Ramos (IMPA, Brazil).

I will describe a famous conjecture, dating back from the 1980s, concerning the way that the electronic energy of an atom or a molecule depends on the number of electrons. Together with Simone Di Marino (Genova) and Mathieu Lewin (CNRS and Paris-Dauphine), we found the first counter-example by going to the semi-classical limit and studying an optimal transport problem. Our nuclei have a fractional charge and the conjecture remains open for integer charge systems, however.

Title: The Precedence-Constrained Family Traveling Salesman Problem

Speaker:  Raquel Bernardino, Department of Mathematics, Lisbon School of Economics and Management (ISEG)

Date | Time: April 8, 2026 | 14h30

Place: NOVA FCT,

Abstract:

We introduce the Precedence-Constrained Family Traveling Salesman Problem (PC- FTSP), which generalizes the FTSP by adding precedence relations between families. The PC-FTSP arises in warehouse order picking with scattered storage, where heavier items must be picked before lighter ones. We propose several formulations and compare them theoretically and empirically. We also derive valid inequalities that strengthen the linear programming (LP) relaxations. As some formulations are non- compact, we design a branch-and-cut algorithm to solve them. Results show the non- compact formulations outperform the compact ones, and the inequalities effectively strengthen the LP bounds on our instances.

Room 1.12 Building VII
   
Abstract: In this talk we will address the lifting problem for the Černý conjecture: namely, whether the validity of the conjecture for a quotient automaton can always be transferred (or “lifted”) to the original automaton. Although a complete solution remains open, we show that it is sufficient to verify the Černý conjecture for three specific subclasses of reset automata: radical, simple, and quasi-simple.  Our approach relies on establishing a Galois connection between the lattices of congruences and ideals of the transition monoid. This connection not only serves as the main tool in our proofs but also provides a systematic method for computing the radical ideal and for deriving structural insights about these classes.  
This is a joint work with Prof. Emanuele Rodaro.

Wave scattering is present in many applications regarding non destructive testing, namely medical imaging. In particular, in the context of inverse scattering problems, the goal is to find unknown properties of the obstacle (scatterer) from the knowledge of the incident field and the measurement of the scattered field or far-field pattern. In this talk, we will focus on numerical methods to solve mathematical models for time-harmonic scattering problems. We will focus on new approaches to ensure stability of the method of fundamental solutions to solve the direct problem and in numerical methods that deal with the ill-conditioning and nonlinearity of the inverse problem, in a time-harmonic wave propagation context. Finally, we will consider a numerical approach for a toy model for elastography, a medical imaging modality used for biological tissue imaging, focusing on their applications in the retina.

Room 1.12 ed. VII 
 
Abstract:  A minimal generating set of a group is a set of elements that generates the group such that, if any element is removed, the remaining set no longer generates the group. For example, the symmetric group of degree n has minimal generating sets whose sizes range from 2 up to n−1. The study of minimal generating sets is a topic of particular interest because of its connections with two important areas: discrete geometry and computational algebra. In discrete geometry, there is a well-known one-to-one correspondence between certain minimal generating sets of involutions satisfying specific axioms and regular polytopes. In computational algebra, the connectivity of product replacement graphs, an important tool used in algebra systems to generate random elements of groups, depends on the parameters m(G) and d(G), which denote the maximal and minimal sizes of minimal generating sets of a group G, respectively.

In this seminar, I will give an overview of the topic and discuss some of its main results and applications.

This talk presents a numerical study of a system of partial differential equations consisting of a parabolic, an elliptic, and a hyperbolic equation, that be used to describe cell migration in elastic tissues by integrating chemotaxis, interstitial fluid pressure, and tissue displacement. In this framework, the system couples a Keller–Segel-type model for cell density and chemical concentration with an elliptic equation for fluid pressure and a wave-type equation for tissue displacement. Cell transport is driven by a nonlinear convective velocity that depends on the chemoattractant gradient, Darcy flow induced by the pressure field, and the tissue displacement velocity, while chemoattractant transport is advected only by Darcy flow. We propose a semidiscrete finite difference method on nonuniform grids, which can be seen as a fully discrete-in-space piecewise linear finite element method. Using an appropriate discrete norm, we establish second-order spatial error estimates for all variables. Finally, we present numerical simulations illustrating the theoretical results and the interplay between chemotaxis and tissue mechanics.

Statistics and Risk Management Seminar

Department of Mathematics, NOVA MATH/FCT NOVA

Title: A computational tool for unsupervised variable selection and patient stratification

Speaker: Roberta Coletti, NOVA Math

Date | Time: May 04, 2026 | 12:00

Location: VII-1.11

Teams: https://teams.microsoft.com/meet/36124291051668?p=9wzuxJVsdpJQkGb9ww

Abstract: In this study, we developed TRIM-IT, a computational framework for data-driven patient stratification and biomarker discovery based on high-dimensional omics data. To address the challenges associated with high dimensionality, TRIM-IT first performs unsupervised variable selection to reduce data complexity while preserving dataset structure. The selected variables are then used for unsupervised clustering and downstream analyses to characterize the identified patient groups. Applied to glioblastoma transcriptomics data, TRIM-IT uncovered three distinct patient clusters associated with tumor histology, significantly different survival outcomes, and molecular profiles suggestive of potential biomarker candidates. 

Short Bio: Roberta Coletti studied mathematics at Sapienza University of Rome. She completed a PhD in mathematics at the University of Trento, with a thesis on ordinary differential equation models of prostate cancer immunotherapy. Between 2021 and 2024, she was a researcher at the Center for Mathematics and Applications at NOVA University of Lisbon. Her work focuses on identifying molecular biomarkers for glioma cancer by analyzing large multi-omics datasets using statistical and machine learning methods. 

Organizers: Isabel Natário and Mina Norouzirad and Marta Lopes

LogosTodos.JPG

This work is funded by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UID/00297/2025 (https://doi.org/10.54499/UID/00297/2025) and UID/PRR/00297/2025 (https://doi.org/10.54499/UID/PRR/00297/2025) (Center for Mathematics and Applications - NOVA Math)

Abstract:
Shigesada, Kawasaki, and Teramoto showed that introducing cross-diffusion effects in the spatial Lotka–Volterra competition
model can destabilise the spatially homogeneous equilibrium and generate spatial patterns. In this seminar, I will present recent work in collaboration with Tommaso Lorenzi and Gaetana Gambino, in which we examined the effect of phenotype heterogeneity in competing populations. In particular, in our modelling framework, phenotype diversity affects movement and interactions between individuals.
Motivated by cellular plasticity, we considered a regime of rapid phenotype switching and derived conditions for cross-diffusion- and phenotype-driven instabilities. Finally, I will present numerical simulations to illustrate the role of the phenotype distribution and its impact on competitive outcomes.

This Seminar is funded by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P.,  under the scope of the projects \href{https://doi.org/10.54499/UID/00297/2025}{\textcolor{blue}{UID/00297/2025}} and \href{https://doi.org/10.54499/UID/PRR/00297/2025}{\textcolor{blue}{UID/PRR/00297/2025}} (Center for Mathematics and Applications

Title: Nearest Correlation Matrices via Halfspace Projections  
Speaker: Yunier Bello-Cruz, Department of Mathematical Sciences at Northern Illinois University (NIU), IL, USA
Date | Time: May 6, 2026 | 14h30 
 

Abstract:

The nearestcorrelation matrix problem asks for the closest positive semidefinite matrixwith unit diagonal to a given symmetric matrix G, measured in the Frobeniusnorm. We introduce HBAP (Halfspace Best-Approximation Projection), aprojection-based algorithm that approximates the positive semidefinite cone byintersections of supporting halfspaces and computes iterates via projectionsonto these simpler sets. At each iteration, HBAP constructs two halfspaces, asupporting halfspace for the positive semidefinite cone derived from thesquared-distance function, and a localization halfspace that enforces monotoneprogress, and projects the anchor point onto their intersection with theunit-diagonal affine subspace. Every iterate satisfies the unit-diagonal constraintby construction. We prove that HBAP is well defined and that the full sequenceconverges to the nearest correlation matrix to G. The projection subproblem ateach step admits a closed-form reduction to a 2X2 linear complementarityproblem, yielding an explicit update formula. Alternatively, the sameprojection can be computed via Dykstra-type inner iterations, for which wederive a natural splitting with fully explicit projectors.

Room: to be announced
 
Abstract: Algorithms and programs for computing the k-universal transversal property of a permutation group G are described. This property gives information about the regularity of a transformation semigroup <G,t> generated by G and a transformation t. New results obtained by the programs are also described.

In this seminar, we present sufficient conditions for the convergence of asymptotic systems in non-autonomous Cohen-Grossberg neural network models that incorporate both infinite discrete time-varying and distributed delays. The main stability criterion is obtained by imposing conditions under which the non-delay terms asymptotically dominate the delay terms. As an application, we provide sufficient conditions ensuring that all solutions of a non-periodic neural network model with unbounded delays converge to a periodic function as time goes to infinity. A numerical example is presented to illustrate the effectiveness of the new results. This is a joint work with A. Elmwafy (PhD student) and César M. Silva of University of Beira Interior, Portugal.

Abstract:

Several strategies are described and analyzed to speed-up gradient-type methods when applied to the minimization of strictly convex quadratics and strictly convex functions. The proposed techniques focus on relaxing the traditional optimal step length associated with gradient methods, including the steepest descent (SD) and the minimal residual (MR) methods. Such a relaxation avoids the well-known negative zigzag effect and allows the iterates to move in the entire space which in turn implies that every so often the search direction approaches some eigenvector of the underlying Hessian matrix. The proposed speedups then rely on taking advantage of the properties of the Lanczos method once a search direction that approaches an eigenvector has been identified in order to accelerate the convergence towards the global minimizer. After analyzing the proposed strategies, we illustrate them on the global minimization of strictly convex functions.

How do we control the sublinear Hardy–Littlewood maximal operator in non-Euclidean settings?  By trading it for linear alternatives.  In this talk, we show that the operator's boundedness on variable Lebesgue spaces over spaces of homogeneous type is entirely characterized by the uniform boundedness of specific averaging operators over dyadic cubes.  Adapting Lars Diening's 2005 Euclidean framework, we expose the mechanics behind this clean reduction: Musielak–Orlicz spaces, Hytönen–Kairema adjacent grids, and the omnipresent principle of self-improvement.

Abstract:

In this work, we study two-stage distributionally robust mixed-integer programs with uncertain parameters having finite discrete support. This setting is particularly attractive from a computational perspective because the DRO problem remains tractable and can be reformulated as a (possibly much larger) mixed-integer program, allowing the use of standard optimization technology. We propose an ambiguity set defined through a generalized optimal transportation problem. This formulation extends the classical Kantorovich ambiguity set, enabling the modeling of a wider range of practical situations while preserving useful structural properties. We analyze the main characteristics of this ambiguity set and discuss how they affect the structure of the resulting optimization problem.

Three solution frameworks are investigated. The first is the Benders-like method proposed by Bansal, Huang, and Mehrotra (2018). The second derives a single-stage formulation obtained by dualizing the transportation problem defining the ambiguity set. The third uses an epigraph formulation with dynamically generated optimality cuts in a row-and-column generation scheme. The approaches are evaluated on a distributionally robust location–transportation problem with uncertain demand. Computational results show that the relative performance of the approaches depends strongly on the characteristics of the ambiguity set: the dualization approach is simple and effective in the easiest instances, the row-and-column generation performs well when the ambiguity set approximates robust optimization, and the Benders-type method is preferable in the remaining settings.

This talk presents  a general theory for coupled systems, with regular and singular nonlinear fully differential equations of higher order, with generalized impulsive effects, depending on both variables and some derivatives. Two types of results are shown: first, an existence theorem, proved via fixed point theory. Secondly, we define a new type of coupled lower and upper solutions, and sufficient conditions to get the localization of a solution and some of its derivatives. The method is based on considering an auxiliary, truncated, and perturbated problem, whose solutions are also solutions of the initial problem. These results are applied to systems of singular Laplacians.

Abstract: Let G be a simple graph and k a positive integer. Two important graph operations are the k-th graph power of G and the complement graph of G. We explore a permutation between both operations and how it affects the independence number of the resultant graphs.

We will discuss local aspects of Banach space theory arising in finite-dimensional Banach spaces of analytic polynomials. The lecture will focus on how classical constants, such as projection constants, unconditional basis constants, and Gordon-Lewis constants, reflect the geometry of these polynomial spaces. I will explain the main ideas behind recent estimates and indicate how they connect local Banach space theory with complex analysis, probability, and combinatorial methods. The lecture is based on joint works with A. Defant, D. Galicer, M. Mansilla, and S. Muro.

Please see the attached PDF for the abstract.

https://drive.google.com/file/d/1V1smOS2b67Hm6UyL2hMkJRqDLSXhL7BH/view?usp=sharing

Abstract:  The identity checking problem asks whether an identity holds in a given semigroup. In this talk, we discuss the identity checking problem for diagram monoids, focusing on twisted partition monoids. We present a structural approach based on an embedding of the twisted partition monoid into a larger regular monoid satisfying the same identities. Using this approach, we show that for every n ≥ 5, the identity checking problem in the twisted partition monoid (P_n^\tau) is co-NP-complete.

https://eventos.fct.unl.pt/novamath_thematic_weeks/pages/seminars

https://eventos.fct.unl.pt/novamath_thematic_weeks/pages/seminars

https://eventos.fct.unl.pt/novamath_thematic_weeks/pages/seminars

Speaker: Weining Wang, University of Bristol

Abstract:

This two-lecture module introduces students to time series analysis and its modern extensions using deep learning and generative AI. The first lecture covers classical stochastic models (AR, MA, ARIMA) and fundamental concepts such as stationarity, forecasting, and model identification. The second lecture bridges traditional time series methods with modern AI approaches, focusing on Transformer architectures for sequence modeling and Diffusion models for generative time series tasks. The module emphasizes conceptual understanding, methodological connections, and practical relevance in economics and data science.

https://eventos.fct.unl.pt/novamath_thematic_weeks/pages/seminars

Speaker: Weining Wang, University of Bristol

Abstract:

This two-lecture module introduces students to time series analysis and its modern extensions using deep learning and generative AI. The first lecture covers classical stochastic models (AR, MA, ARIMA) and fundamental concepts such as stationarity, forecasting, and model identification. The second lecture bridges traditional time series methods with modern AI approaches, focusing on Transformer architectures for sequence modeling and Diffusion models for generative time series tasks. The module emphasizes conceptual understanding, methodological connections, and practical relevance in economics and data science.

https://eventos.fct.unl.pt/novamath_thematic_weeks/pages/seminars

https://eventos.fct.unl.pt/novamath_thematic_weeks/pages/seminars

Statistics and Risk Management Seminar (double session)

Department of Mathematics, NOVA MATH/FCT NOVA

Seminar I

Title: Induced nonparametric ROC surface regression

Speaker: Vanda Inácio; University of Edinburgh, Scotland

Date | Time: July 14, 2026 | 14:00

Location: Hangar II, room 2

Teams: https://teams.microsoft.com/meet/36124291051668?p=9wzuxJVsdpJQkGb9ww

Abstract: The receiver operating characteristic (ROC) surface is a popular tool for evaluating the discriminatory ability of diagnostic tests measured on a continuous scale when there exist three ordered disease groups. Motivated by the impact that covariates may have on the diagnostic accuracy, and to safeguard against model misspecification, we develop a flexible model for conducting inference about the covariate-specific ROC surface and its functionals. Specifically, we postulate a location-scale regression model for the test outcomes in each of the three disease groups where the mean and variance functions are estimated through penalised-splines, while the distribution of the error term is estimated via a smoothed version of the empirical cumulative distribution function of the standardised residuals. Our simulation study shows that our approach successfully recovers the true covariate-specific volume under the surface and optimal pair of thresholds in a variety of scenarios. Our methods are motivated by and applied to data derived from an Alzheimer's disease study and we seek to assess the accuracy of several  biomarkers to distinguish between individuals with normal cognition, mild cognitive impairment, and dementia and how this discriminatory ability may change with the age and gender.

Seminar II

Title: Extremal Vulnerability

Speaker: Miguel de Carvalho; University of Edinburgh & University of Aveiro

Date | Time: July 14, 2026 | 15:30

Location: Hangar II, room 2

Teams: https://teams.microsoft.com/meet/36124291051668?p=9wzuxJVsdpJQkGb9ww

Abstract: In many complex systems, identifying the most vulnerable component is essential for effective prevention, intervention, and risk management. In this talk, I will introduce the notion of extremal vulnerability, defined as the long run tendency of a component to be affected by extreme events occurring in other components. The proposed framework builds on the tail dependence matrix and introduces the Extremal Vulnerability Rank (XVRank) method—a PageRank-inspired algorithm designed to quantify extremal vulnerability.  We establish the theoretical properties of the proposed inferences, including consistency and asymptotic normality, and validate their performance through Monte Carlo simulations. The proposed methods are illustrated using financial data to determine assets most exposed to severe market downturns. Joint work with P. Redondo, R. Huser, and H. Ombao (KAUST).

Organizers: Isabel Natário and Mina Norouzirad and Miguel Fonseca

LogosTodos.JPG

This work is funded by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UID/00297/2025 (\url{https://doi.org/10.54499/UID/00297/2025}) and UID/PRR/00297/2025 (\url{https://doi.org/10.54499/UID/PRR/00297/2025}) (Center for Mathematics and Applications)

Abstract:

Derivative-freeoptimization (DFO) is essential for problems where derivatives are unavailableor expensive to compute, but its scalability is limited by the high cost ofmodel construction in large dimensions. Subspace techniques address thischallenge by building models and performing optimization in low-dimensionalaffine subspaces.  This talk presents aunified view of subspace modelling and methods for DFO.  We first establish theoretical connectionsbetween full-space and subspace linear and quadratic models and simplexderivatives, showing that they coincide on the underlying subspace and alongorthogonal directions.  We then presentrandom subspace trust-region methods that leverage these models, includingframeworks with provable convergence and complexity guarantees forunconstrained and convex-constrained problems.