Séminaire équipe EMA

Le séminaire de l'équipe Équations aux dérivées partielles, Modèles aléatoires et Approximation à lieu chaque jeudi après midi, généralement à 13h30.

Responsables : Christophe Bourel et Michel Davydov.

Liste des exposés de 2026

• Jeudi 3 décembre 2026

  Davide Giraudo (Université de Strasbourg)

  TBA (⊕ résumé)

  TBA

  13:30 - 14:30

• Jeudi 25 juin 2026

  Dimitri Shepelsky (B. Verkin Institute for Low Temperature Physics and Engineering (Ukraine))

  A Riemann–Hilbert approach to the Short Pulse equation: non-regular Solutions, I (⊕ résumé)

  We study initial and initial boundary problem for the Short Pulse equation, which is an integrable PDE arising in nonlinear modeling the propagation of ultra-short optical pulses. The model is integrable in the sense that it can be treated by the Inverse Scattering Transform method (a.k.a. the Nonlinear Fourier Transform). The emphasis will be made on modeling non-regular (particularly, discontinuous) waves. We show that non-regular features of such solutions are due to the change of variables relating the Short Pulse equation to another integrable PDE -- the sine-Gordon equation.

  13:30 - 14:30

• Jeudi 25 juin 2026

  Iryna Karpenko (Université de Vienne)

  A Riemann–Hilbert Approach to the Short Pulse Equation: Nonregular Solutions II (⊕ résumé)

  We study initial and initial boundary problem for the Short Pulse equation, which is an integrable PDE arising in nonlinear modeling the propagation of ultra-short optical pulses. The model is integrable in the sense that it can be treated by the Inverse Scattering Transform method (a.k.a. the Nonlinear Fourier Transform). The emphasis will be made on modeling non-regular (particularly, discontinuous) waves. We show that non-regular features of such solutions are due to the change of variables relating the Short Pulse equation to another integrable PDE -- the sine-Gordon equation.

  14:30 - 15:30

• Vendredi 19 juin 2026

  Marcos Raydan (Universidade Nova de Lisboa, Portugal)

  Derivative-free optimization approach for structured symmetric matrices with fixed eigenvalues (⊕ résumé)

  A Derivative-Free Optimization (DFO) model is developed and analyzed for solving inverse structured symmetric matrix problems for which the eigenvalues are specified. Some (zero and nonzero) entries are preassigned and cannot be changed, while others should be nonzero but their values are not given. The rest of the entries are completely free. The obtained matrix must meet these criteria and have the specified eigenvalues. This specialized inverse eigenvalue problem is relevant to various applications and is linked to determining the graph, with weights on the undirected edges, of the matrix associated with its sparse pattern. Our novel optimization model requires computing the eigenvalues of a symmetric matrix to evaluate the non-differentiable objective function. We apply deterministic DFO schemes, specifically the global variant GLODS of the well-known family of directional direct search (DDS) methods. We discuss its convergence properties which are based on the fact that the bjective function of our model is Lipschitz continuous. Additionally, we explore the potential benefits of using several well-established heuristic strategies to solve the proposed optimization model. We present preliminary numerical results to illustrate and compare the performance of the considered deterministic and heuristic DFO options in various possible scenarios.

  10:10 - 11:10 B014

• Vendredi 19 juin 2026

  Lothar Reichel (Kent State University, USA)

  Gauss-type quadrature rules: error estimation and computation (⊕ résumé)

  Many problems in science and engineering require the evaluation of integrals. Gauss quadrature rules provide a popular tool for approximating integrals with respect to a nonnegative measure on a real interval. It is important to estimate the quadrature error when applying a Gauss quadrature rule in order to assess whether whether the quadrature error is sufficiently small. The classical approach to estimate this error is to evaluate both the Gauss rule and an associated Gauss-Kronrod rule, and use the difference in the computed quadrature values as an estimate of the quadrature error in the Gauss rule. However, Gauss-Kronrod rules have several shortcomings such as they might not exist. This has promted the development of a variety of alternatives to Gauss-Kronrod rules. This talk reviews these alternative quadrature rules and discusses their computation.

  11:00 - 12:00 B014

• Jeudi 18 juin 2026

  Laurent Smoch (LMPA)

  Simuorb: a new method for generating and describing the intersection points of clique-arrangements

  14:00 - 15:00

• Jeudi 21 mai 2026

  Omar Rhouni (LMPA)

  Birkhoff Matrix Polynomial Interpolation Problem, Algorithmic Aspect (⊕ résumé)

  Given a list $Z_n = [z_0, ..., z_n]$ with $(n + 1)$ distinct nodes, of $K = \mathbb{R}$ or $\mathbb{C}$, we will study the existence and uniqueness of a $s \times m$ matrix polynomial $P$ such that $P$ and a number of its derivatives take, in these nodes, given values. Recently, Messaoudi and Sadok presented a new algorithm for computing the Hermite matrix interpolation polynomial called the Generalized Recursive Matrix Polynomial Interpolation Algorithm (GRMPIA). In this presentation, we presented a new formulation of the Birkhoff matrix polynomial interpolation problem and derived a new algorithm called the Recursive Hermite-Birkhoff Matrix Polynomial Interpolation Algorithm (RHBMPIA) to solve the Birkhoff interpolation problem and extend the GRMPIA.

  13:30 - 14:30 100% visio

• Jeudi 2 avril 2026

  Laetitia Colombani (Université de Lyon 1)

  Asymptotic properties of inhibitive Hawkes process and cumulative process (⊕ résumé)

  Hawkes process was introduced by Hawkes in 1971 and are widely used in many applications (earthquakes, neurons, social network, finance, etc). This jump process has an intensity which depends on the past. Linear 'self-exciting' Hawkes process has been particularly studied and some asymptotic results are well-known. I study non-linear Hawkes processes, which can model self-inhibition and self-excitation. We proved asymptotic properties (law of large numbers, CLT, large deviations), by considering a new point of view for this process: the renewal structure of Hawkes process, introduced by Costa, Graham, Marsalle and Tran (2020), leads to a comparison with cumulative processes. In this talk, I'll introduce Hawkes processes and cumulative processes. By exhibiting their link, I'll give an idea of the approach we use to prove asymptotic properties.

  13:30 - 14:30 TBA

• Jeudi 12 mars 2026

  Apolline Louvet (INRAE Avignon)

  Stochastic modelling of population dynamics in a spatial continuum and application to epidemiology (⊕ résumé)

  Spatial Lambda-Fleming-Viot processes, or SLFVs, are a family of stochastic processes that have been developed to overcome some issues arising when defining stochastic population dynamics models in a spatial continuum of arbitrary dimension. Their main characteristic is their ''reproduction event-driven'' dynamics that controls local reproduction rates and ensures the existence of a dual process, which is a key tool to the analysis of SLFV processes. In this talk, after giving an overview of this modelling framework, I will present a recent extension to the modelling of epidemics, giving rise to a stochastic SIS-type model in continuous space. I will show to what extent the central concept of basic reproduction number can be extended to this model, using the duality relation along with the characterization of the process as the unique solution to a martingale problem. Based on a joint work with Bastian Wiederhold (LMU).

  13:30 - 14:30 C107

• Jeudi 5 mars 2026

  Daniele Avitabile (VU Amsterdam)

  Noise-induced pattern formation in networks of spatially-dependent neural networks (⊕ résumé)

  This talk presents a study of pattern formation in a class of high-dimensional neural networks defined on random graphs and subjected to spatio-temporal stochastic forcing. The connectivity matrices of these neural networks are randomly generated and can be excitatory or inhibitory, dense or sparse, and need not be symmetric. Under generic conditions on coupling and nodal dynamics, we prove that the network admits a rigorous mean-field limit, resembling a Wilson-Cowan neural field equation. The state variables of the limiting system are the mean and variance of neuronal activity. We select networks with tractable mean-field equations and perform a bifurcation analysis using the diffusivity strength of the afferent white noise on each neuron as the control parameter. We identify conditions for Turing-like bifurcations in a system where the cortex is modeled as a ring and provide numerical evidence of noise-induced spiral waves in models with a two-dimensional cortex. We present numerical evidence that solutions of the finite-size network converge weakly to those of the mean-field model. If time permits, I will discuss recent extensions of this work that involve dynamics on the network weights, and the employment of Wilson-Cowan neural field-type equations in data assimilation problems.

  13:30 - 14:30 C104

• Jeudi 5 février 2026

  Nicolas Beuvin (LAMFA (Amiens))

  Résultats de classification des solutions de l'équation de Poisson semi-linéaire dans des domaines non-bornés. (⊕ résumé)

  Résumé du séminaire: Dans ce séminaire, je vais m'intéresser aux solutions positives de l'équation suivante: $$-\Delta u=f(u) \quad \text{dans } \Omega,$$ où $f$ est une fonction de classe $C^{1}$ et $\Omega$ est un domaine non borné et où l'on a imposé des conditions de Dirichlet homogène sur le bord. L'idée est de classer de telles solutions en fonction de leurs propriétés géométriques (unidimensionnelles, nulles, $\dots$). L'exposé sera divisé en deux parties, une première partie introductive où je présenterai les résultats existants dans ce cadre, et une seconde partie où j'énoncerai de nouveaux résultats que l'on a mis en évidence en collaboration avec A. Farina et B. Sciunzi.

  13:30 - 14:30 C107

• Jeudi 15 janvier 2026

  Abderrahman Bouhamidi (LMPA)

  Séminaire commun avec ADA

  14:00 - 15:00

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