Title: Numerical methods for delay and fractional differential equations.

Speaker: Neville J. Ford* (University of Chester, UK).

Date| Time: Friday, 18 October 2024, from 14:15 to 16:15 – Room 3.2, building VII.

Abstract: We will consider how to solve delay differential equations and fractional differential equations using numerical schemes. To understand how to do this, we will begin by considering the fundamental theory associated with these equations. We look at the dimension of the underlying dynamical systems to explain how approximation schemes should be set up, and how their performance should be judged. In particular, we shall look at initial and boundary conditions needed to ensure a unique solution and we will see how these must be related to the numerical schemes. If time permits, we shall consider some fractional problems with delays and see how the insights from both types of problems combine in this case.

*https://www.researchgate.net/profile/Neville-Ford

Title: A mathematical framework for dynamical social interactions with dissimulation.

Speaker: Max O. Souza (Center for Mathematics and Applications (NOVA Math), NOVA FCT, Universidade NOVA de Lisboa, Portugal).

Time: Wednesday, 23 October 2024, from 14:15 to 15:15.

Place: Room 1.6, building VII.

Abstract: Modeling social interactions is a challenging task that requires flexible frameworks. For instance, dissimulation and externalities are relevant features influencing such systems — elements that are often neglected in popular models. This paper is devoted to investigating general mathematical frameworks for understanding social situations where agents dissimulate, and may be sensitive to exogenous objective information. Our model comprises a population where the participants can be honest, persuasive, or conforming. Firstly, we consider a non-cooperative setting, where we establish existence, uniqueness and some properties of the Nash equilibria of the game. Secondly, we analyze a cooperative setting, identifying optimal strategies within the Pareto front. In both cases, we develop numerical algorithms allowing us to computationally assess the behavior of our models under various settings. Joint work with Y Saporito and Y Thamsten.