• Augustin Leclerc - Modal computation for an open electromagnetic eigenvalue problem - Mardi 28 mai 2024, 13h30
  The study of electromagnetic (EM) wave propagation is essential for investigating the impact of human technologies on the environment. For example offshore wind energy is transported by dynamic twisted cables, whose armouring prevents the propagation of a significant proportion of the waves. Nevertheless, what remains escapes from the cable, and our aim here is to study its diffusion in the vast expanse of sea water.
  To consider this problem, we propose to model the cable and the surrounding water by an open 3D waveguide, which is an invariant domain according to the cable direction and which is unbounded in the two other directions. Hence, we will take a modal approach for the resolution, with Absorbing Boundary Conditions (ABC) around the section of the cable.
  First, we present the simplified model of open Helmoltz eigenproblem. Especially, we will discuss how to efficiently linearize the ABC w.r.t. the eigenvalue. Then, we will consider the adaptation of the boundary condition to the Maxwell eigenproblem.
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• Audrey Chaudron - Exceptional Configurations in a Boolean Model - Mardi 14 mai 2024, 13h30
  Firstly, I will explain my thesis topic and the motivations driving us to study this problem. Secondly, I will describe how we approached this problem.

My thesis aims to investigate exceptional point configurations in a Boolean model in different settings. More precisely, in a homogeneous Poisson process in which two points are connected if they are at a distance less than or equal to a fixed real number, we examine the connected components from both a probabilistic perspective (probability of having a cluster of k points) and a geometric perspective (given the realization of a cluster of k points, is there a preferential shape for this cluster). My thesis topic deals with these questions when the intensity of the process converges to 0 in a Euclidean framework and simultaneously in a hyperbolic framework when the intensity explodes. The motivations behind choosing these frameworks will become apparent in the applications and when we discuss the works of K. Alexander.

Regarding the approach to this problem, we will see how the knowledge of a limiting shape helps for solving  the probabilistic questions.
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• Bahae-Eddine Madir - Physics informed neural networks for Stefan problem - Mardi 16 avril 2024, 13h30
  Physics-informed deep learning has drawn tremendous interest in recent years to solve computational physics problems, whose basic concept is to embed physical laws to constrain/inform neural networks, with the need of less data for training a reliable model. In this presentation, we introduce physics-informed neural networks (PINNs) and we explore the resolution of the Stefan problem using this method.
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• Sara Vegetti - Generalized Nash Equilibrium Problems with Unawareness - Mardi 12 mars 2024, 13h30
  Game Theory is a discipline that we hear more and more about in different areas. This survey aims to study two concepts in this discipline, generalized Nash equilibrium and unawareness in static games. Generalized Nash equilibrium problems model situations in which each player's strategy space depends on the other agents' choices. While unawareness refers to models that represent the situation in which players don't have full knowledge of the game, leading to the emergence of subjective games. The main goal of this talk is to propose notions of equilibrium in games with unawareness, as well as numerical methods to solve them.
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• Averil Prost - Tropical heat: A (max ,+) point of view on the Poisson equation - Mardi 30 janvier 2024, 14h00
  The (max,+) semialgebra relies on a particular choice of operations that belongs to the realm of idempotent analysis. In this short talk, we introduce these operations and the dialog between them and classical algebra. As an application, we give the (max,+) parallel to the heat equation.