This talk provides an overview of Evolutionarily Stable Strategies (ESS) in population games and addresses some common misconceptions found in the classical literature. We focus specifically on Locally Superior Strategies (LSS), which represent a very special case of ESS, examining them in contexts with both finite and infinite action sets. Locally Superior Strategies are particularly significant among evolutionary stability concepts because they act as attractors under the Replicator Dynamic. The main result I will present unifies the finite and infinite frameworks by establishing a necessary and sufficient condition for an ESS to be a LSS.

We have been studying compartmental models of infectious disease spread, considering voluntary vaccination. The law governing the dynamics of voluntary vaccination is defined such that each individual chooses whether or not to be vaccinated, influenced by their perception of the choices of other individuals and the state of the disease in the system. This is known in the literature as imitation dynamics. I will present a simple model that explains the main ideas behind the construction of this type of model. The use of imitation dynamics in this model led to the emergence of chaotic behavior. I will also present two other models, one with an age structure and the other with loss of immunity.

Free transmission problems form a class of free boundary problems in which the solution-dependent discontinuity occurs at the level of the operator. Arising naturally in the modelling of heterogeneous diffusion and related processes, these problems present genuine mathematical difficulties, especially in the fully nonlinear setting. I will discuss recent progress on the existence of viscosity solutions and on their optimal regularity, both in the interior and up to the (fixed and free) boundary. I also plan to mention a few results on the development of numerical schemes tailored to this class of problems. Time permitting, I will conclude with a selection of open questions and possible directions for future research.

Speaker: Prof. Marta Gomes, Instituto Superior Técnico, University of Lisbon

Date | Time: December 5, 2025 | 14h30

Place:NOVA FCT, Departamento de Informática , sala232

Title: Spatialmulti-criteria decision analysis for rehabilitation priority ranking: acollaborative application to heritage workforce housing sites ( Co-authors: AnaPaula Falcão, Rita Machete, Alexandre B. Gonçalves )

Abstract: This workpresents a methodology to rank heritage sites regardingrehabilitation,considering both the characteristics of building sites and ofthe urban environment in the surrounding area. The objective is to aid thedecision process of building rehabilitation byranking the sites according totheir potential for re-emergence in the affordable housing rental market. Thedeveloped methodology is based on a combination of multi-criteria decisionanalysis (MCDA) and spatial analysis of geographical data, in order toconstruct an index, the “rehabilitation potential”, which is understandable byrehabilitation technicians and land managers and is applicable to support a listof priorities of building rehabilitation interventions. The methodology wasapplied to a case study consisting of aset of 33 heritage sites of theworkforce housing typology in Lisbon. These were built in the early industrialage in Portugal and are owned by the city municipality. The application ofMCDAwas a collaborative process that brought together the expertise of the academyand of the public administration. The results included a sensitivity analysisand gave form to a recommendation of five sites, selected from the totalworkforce housing set, to be rehabilitated in the near future.

Short bio: Prof. Marta Gomes is anAssistant Professor at Instituto Superior Técnico (IST), Department of CivilEngineering, Architecture and Environment, and a researcher at CERIS. She holdsa PhD in Systems Engineering (2007) from IST and has extensive expertise inoperations research, optimization, discrete-event simulation, multi-criteriadecision analysis, and large-scale data analytics, with applications acrosscivil engineering, industrial engineering, mechanical and aerospace systems.Her career includes a strong record of publications and collaborative research projects inmaintenance optimization, transport systems, pavement engineering, and urbanand environmental planning. 

Title: Fractional Derivatives: Applications in data fitting and Artificial Neural Networks.

Speaker: Prof. Hamza El Mahjour (Abdelmalek Essaâdi University, MA).

Date | Time: December 10, 2025 | from 14:00 to 14:30.

Place: Room 2.23 - Building IX.

Abstract: Fractional calculus introduces non-integer-order derivatives with a built-in memory effect, enabling more accurate modeling of history-dependent phenomena than classical integer-order derivatives.This talk focuses on that memory property and its practical impact. A clear example is the work of Barros et al. (2021): a fractional Caputo SIR model for COVID-19 that incorporates transmission hysteresis and reduces fitting errors by 10-20\% on real data (Italy, South Korea) compared to the standard SIR model, using an adapted Adams–Bashforth–Moulton scheme.I will also briefly review the integration of fractional derivatives into artificial neural networks. By employing Caputo-type fractional operators, these networks gain memory-dependent dynamics and additional tunable parameters (the fractional orders), leading to improved accuracy, stability, adaptability, and ability to capture long-range dependencies in tasks from control and modeling to image processing and medicine.Overall, the memory effect of fractional derivatives provides tangible advantages in both epidemiological modeling and next-generation neural networks, making complex systems easier to represent and control.

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Title: An Introduction to Fractional Calculus: Theory and Challenges.

Speaker: Prof. Aadil Lahrouz (Abdelmalek Essaâdi University, MA).

Date | Time: December 10, 2025 | from 14:30 to 15:00.

Place: Room 2.23 - Building IX.

Abstract: This talk gives an introduction to fractional calculus, which extends classical calculus to non-integer orders. We start with the basic concepts, including the definitions of fractional integrals and fractional derivatives. We focus mainly on two approaches: the Riemann-Liouville and Caputo definitions. We explain their main properties and the key differences between these formulations in different function spaces. Next, we present the main theory of fractional differential equations. We cover existence and uniqueness results, continuation and blow-up theorems. We also explain how fractional differential equations differ from classical ones, particularly in their memory effects and non-local behavior. Throughout the presentation, we point out several important theoretical challenges and open questions in the field.

MatHBioS Workshop

Title: Initiation to Neural Networks with PyTorch.

Speaker: Prof. Hamza El Mahjour (Abdelmalek Essaâdi University, MA).

Date: December 9, 2025 | from 10:00 to 12:00 and from 14:30 to 15:30.
          December 10, 2025 | from 10:00 to 12:00.
          December 11, 2025 | from 14:30 to 15:30.

Place: Room 2.23 - Building IX.

Abstract: This training is designed for PhD students with prior Python experience. It is a five-hour workshop that introduces participants to the practical implementation of neural networks using PyTorch, with a strong emphasis on hands-on coding and real-time model development. Designed for those already familiar with Python, the sessions will guide you from foundational concepts to building, training, and evaluating deep learning models. Through interactive exercises, participants will gain confidence in using PyTorch as a flexible and powerful framework for research applications.

*Those who are interested are invited to complete the form at this link: (https://docs.google.com/forms/d/e/1FAIpQLSckWV1aZjUmXXaW8xieqpTDuxkQSl74OqzZM6cmgQvWWeqdkw/viewform?pli=1)

In this talk, we revisit compartmental models, given by systems of ordinary differential equations, that describe the transmission dynamics of specific infectious diseases. These models are then generalized through hybrid frameworks and complex networks, enabling their application to a large number of evolution problems in fields such as sociology, economics, geography and epidemiology. Optimal control methods are applied to these models and complex networks aiming to mitigate epidemic outbreaks. In the second part of the talk, we propose a controlled complex network of Lotka-Volterra systems, where the strength of the migrations of biological populations are represented by control functions, reproducing the implementation of ecological corridors. We establish synchronization-type results, and the solutions to the optimal control problems demonstrate the potential to restore biodiversity in heterogeneous habitats. This is achieved by reaching either a global coexistence equilibrium or, in a more favorable scenario, a global limit cycle-ensuring sustained biological oscillations and vibrant ecological dynamics.

We investigate the unbounded operator obtained from the finite Hilbert transform when it acts from $L^1(-1, 1)$ into itself. A full inversion theorem is established for this operator, together with suitable extended versions of the Parseval and Poincaré-Bertrand formulae.

The talk is based on joint papers with Oleksiy Karlovych. We consider multidimensional generalisations of Wiener-Hopf operators and show that, under mild restrictions on the underlying Banach function space, their norm is estimated below by the L^infinity norm of the symbol, while their Kuratowski measure of noncompactness is estimated below by half that norm. Additionally, we show that for a classical Wiener-Hopf operator on a (separable) translation-invariant Banach function space over the half-line, its Hausdorff measure of noncompactness, its essential norm, and its norm are all equal.

Statistics and Risk Management Seminar

Department of Mathematics, NOVA MATH/FCT NOVA

Title: Estimation of Above-Ground Biomass in Forests Using Satellite Data

Speaker: Ricardo Coelho, PhD Student, NOVA SST, Caparica, Portugal

Date | Time: January 22, 2026 | 14:30

Location: To be announced

Teams: https://teams.microsoft.com/meet/32754086330496?p=nspp91z49enhjNBXTR

Abstract: Monitoring carbon sequestration is essential for climate policy, carbon markets, and ecosystem assessment. Above-Ground Biomass (AGB) is a key indicator of carbon storage, where it can be estimated using direct or indirect methods. Direct methods involve the destruction of the trees, while indirect methods, like allometric equations, require the collection of forest inventory data, which is a time-consuming and costly process. With technological advances, a faster and more cost-effective alternative is to estimate AGB through remote sensing, combining satellite data with field measurements, which can lead to more accurate estimates.Machine learning (ML) models have been widely applied for AGB prediction, but many do not account for spatial autocorrelation and fail to quantify prediction uncertainty. Hybrid approaches that combine spatial statistical models with ML have emerged to address these limitations, leveraging both predictive power and spatial dependency modelling. This study first presents a simulation experiment to systematically compare the predictive performance of ML, hybrid, and spatial statistical methods under controlled geostatistical scenarios. We then apply these approaches to estimate AGB in a region of Spain, using GEOSAT-2 remote sensing data, including reflectance bands, vegetation indices, and texture metrics. 

Short Bio: Ricardo Coelho is a PhD student in the Mathematical Doctoral Programme at the NOVA School of Science and Technology (FCT-NOVA). His research work is focused on predicting forest biomass, through statistical models, using field and remote sensing data. Before enrolling in his PhD, he did a MSc in Mathematics and Applications at FCT-NOVA and a BSc in Mathematics at the same university. 

Organizers: Isabel Natário and Mina Norouzirad

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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)

We study a class of degenerate fully nonlinear elliptic equations consisting of a pure equation and an associated transmission-type free boundary problem. We first propose a regularization of the pure equation and derive a numerical method for the regularized problem. The regularization plays a crucial role in ensuring the monotonicity of the numerical scheme. We prove that the method is monotone, consistent, and stable. As a consequence, the Barles–Souganidis framework guarantees the convergence of the numerical approximation. Once the numerical treatment of the pure equation is established, we show how a similar approach can be extended to the free boundary transmission problem. Finally, we present numerical experiments that support the theoretical results.

In this work, we study the Traveling Purchaser Problem with Incompatibility Constraints (TPP-IC), an NP-hard combinatorial optimization problem that extends the classical Traveling Purchaser Problem (TPP) by introducing incompatibilities between items. These prohibit incompatible items from being transported on the same route. We model the TPP-IC using structures called compatibility graphs, which ensure, by construction, that any feasible route does not transport incompatible items. To address the problem, we propose several two-index mixed-integer linear programming (MILP) formulations, including both item-based and market-based approaches. We present a theoretical and computational comparison of these models. In addition, we introduce a family of valid inequalities that exploit the incompatibility constraints. These inequalities strengthen the formulations and are incorporated into a branch-and-cut algorithm. Our computational experiments show that the two-index formulations based on the compatibility graphs yield significantly higher linear programming relaxation values compared to the three-index formulations in the literature. They also solve more benchmark instances. Our results also highlight the main factors that contribute to the difficulty of solving TPP-IC instances and reveal the limitations of exact solution methods in instances with a high degree of item incompatibility.

Optimal transport is a very versatile theory that lifts the geometry on a given underlying space to the overlying Wasserstein space of probability measures. Based on this rich interpretation, Jordan, Kinderlehrer and Otto showed 25 years ago that the (linear!) heat equation can be seen as the (highly nonlinear!) Wasserstein gradient flow of the Boltzmann entropy in the space of probability measures, thus providing a strong form of the second principle of thermodynamics. This sparked tremendous interest due to the interconnection between various mathematical branches, ranging from applied PDEs, numerical analysis, probability and interacting particle systems, metric geometry, functional analysis, and more. In this talk I will try to review the main ideas behind this formalism, and show how classical optimal transport can be extended to study a broad class of evolution equations from a variational standpoint (eg. Hele-Shaw dynamics, reaction-diffusion, multiphase flows, evolutionary genetics, etc.).

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.

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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.