Membres | CEREMADE - UMR CNRS 7534 - Université Paris-Dauphine

Séminaire

Séminaire des jeunes chercheurs

Intervenant : EICHINGER Katharina (CMAP)
Titre :
The Schrödinger problem aka entropic optimal transport - the statistical mechanics perspective

Le : 02/03/2023 de : 17:00 à : 17:30
In this talk I will present the Schrödinger problem which consists of finding the most likely evolution of (random) particles given a fixed starting and final distribution. This problem has gained a lot of popularity in the past years due to its connection to entropic optimal transport. I will start by giving heuristics on the problem and formally deriving its formulation via a large deviations principle. Then I will show its connection to entropic optimal transport and state some properties of this optimization problem. Finally, if time permits, we will see some applications.
Salle : A707

Séminaire

Séminaire des jeunes chercheurs

Intervenant : ZIVIANI Luca (CEREMADE)
Titre :
Introduction to hypocoercivity for the kinetic Fokker-Planck equation

Le : 23/02/2023 de : 17:00 à : 17:30
In this talk, we will briefly present the concept of Hypocoercivity and its application to the kinetic Fokker-Planck equation. Hypocoercivity is a paramount tool of kinetic theory. Given a PDE of kinetic type, it tries to combine the conservative action of a transport operator and the diffusive action of a collision operator to prove the decay of the solution towards an equilibrium state. The applications of such equations are various, from Physics to Biology, and more generally every model consisting in the transport and diffusion of a certain quantity can potentially be studied by these equations. In the first part of the talk, we will give a quick introduction to the main equations of kinetic theory, emphasizing how hypocoercivity methos allow a decay towards the equilibrium state. In the second part of the talk, we will focus on the kinetic Fokker-Planck equation with general confinement potential and local equilibrium.
Salle : A707

Séminaire

Séminaire des jeunes chercheurs

Intervenant : HUAN Ruihua (CEREMADE)
Titre :
Hawkes process - simulation and estimation

Le : 09/02/2023 de : 17:00 à : 17:30
In this introductory talk, we will discuss the simulation and estimation methods for the self-exciting point processes - Hawkes processes. The first part of this talk will be the essentials of the Hawkes process (we focus on the univariate Hawkes process). And on the second part we talk about some simulation methods, mainly thinning algorithm and cluster algorithm. Then we will turn to the statistical inferences, fitting Hawkes process by MLE, cumulants etc.
Salle : B207

Séminaire

Séminaire des jeunes chercheurs

Intervenant : FU Changqing (CEREMADE)
Titre :
Mechanics, PDE and SDE for Image Generation

Le : 02/02/2023 de : 17:00 à : 17:30
In this talk, we present some recent applications of Image Generation Models with Machine Learning, using ideas from analysis and probability. (1) Variational CNN: How the Lagrangian system is generalized from the physical space to the color spectrum to characterize the CNN layer flow. (2) Perceptual path-integral: A practical improvement from a simple symmetry idea on the Gaussian tensor, to improve the quality of GAN, VAE, Diffusion Models, etc. (3) Diffusion Models: Learning a Backward Stochastic Differential Equation which generates art works, AKA the mathematics of the popular Stable Diffusion and DALL-E. (4) Time permitting, we will present some results on a new application of Optimal Transport in Federated / Transfer Learning of neural networks.
Salle : B207

Séminaire

Séminaire des jeunes chercheurs

Intervenant : LELOTTE Rodrigue (CEREMADE)
Titre :
An introduction to Optimal Transport and its applications to Density Functional Theory in Quantum Chemistry

Le : 27/10/2022 de : 17:00 à : 17:30
I will present Optimal Transport (OT) theory in a very brief manner (e.g. Kantorovich & Monge formulations of OT, duality theory and entropic-regularization). I will then explain how OT naturally arises in Density Functional Theory (DFT), an important computational method in quantum chemistry, and present (if time allows) a discretization & algorithm of mine to solve this problem.
Salle : A707

Séminaire

Séminaire des jeunes chercheurs

Intervenant : BERTRAND Théo (CEREMADE)
Titre :
Distances in data applications

Le : 20/10/2022 de : 17:00 à : 17:30
The goal of this talk is to introduce some problems and techniques in Data-centered applications of Inverse Problem, in particular around imaging and medical imaging as those are my area of expertise. The choice of distances in applications, be that as a simple data term or as a way to descibe interesting geometries, is important. Recent advances, both in mathematics and in hardware, has made it possible to include more geometric information in our frameworks. Our journey will focus around the definition and properties of Optimal Transport and Geodesic distances and the efficient techniques that make them numerically accessible for further developments. Finally, we'll look at a few examples from research that try to leverage the notions introduced.
Salle : A707

Séminaire

Séminaire des jeunes chercheurs

Intervenant : HSU Yueh-Sheng ()
Titre :
Asymptotic of the smallest eigenvalues of the continuous Anderson Hamiltonian in d ? 3

Le : 24/02/2022 de : 17:00 à : 18:30
The Anderson Hamiltonian is a random Schrödinger operator that arises in the physical model of Anderson, which describes the evolution of particles in random media. This operator in discrete setting induces intensive mathematical study since 1990s, as its spectrum and eigenfunctions explain the phenomenon of Anderson localisation. However, due to the irregularity of white noise, the mathematical definition of its continuous counterpart was unclear until the recent introduction of novel SPDE theories. In this work, we consider the continuous Anderson Hamiltonian with white noise potential on (?L/2, L/2)^d in dimension d \leq 3, and derive the asymptotic of the smallest eigenvalues when L goes to infinity. We show that these eigenvalues go to -\infty at speed (log L)^{1/(2?d/2)} and identify the prefactor in terms of the optimal constant of the Gagliardo-Nirenberg inequality. This result was already known in dimensions 1 and 2, but appears to be new in dimension 3. We present some conjectures on the fluctuations of the eigenvalues and on the asymptotic shape of the corresponding eigenfunctions near their localisation centres.
Salle : A707

Séminaire

Séminaire des jeunes chercheurs

Intervenant : PINTO ANASTACIO MACHADO João ()
Titre :
Gradient Flows in the Wasserstein Space and some detours

Le : 17/02/2022 de : 17:00 à : 18:30

Salle : A707

Séminaire

Séminaire des jeunes chercheurs

Intervenant : M?DRY ?ukasz (CEREMADE)
Titre :
Singular ODEs and regularization by noise

Le : 10/02/2022 de : 17:00 à : 18:30
It’s a common knowledge that ODEs driven by vector fields that do not satisfy Lipschitz property in space argument can have multiple solutions. However, as it turns out, adding a noise (Brownian motion) to the equation recovers the uniqueness of solutions, both in a law (weak) and a pathwise (strong) sense. We will briefly discuss the basic case of Brownian motion, which allows us to bring down the regularity of vector fields to continuity. Then we’ll move on to the case of fractional noise, which allows for the negative regularity of a drift. To this end, we’ll introduce averaged operators and nonlinear equations theory, which on top of providing full solution theory give us pathwise stability estimates. We will demonstrate how to recast the original equation as a nonlinear one thanks to the recently introduced stochastic sewing lemma. If time permits, we’ll discuss which properties of fractional Brownian motion appear to be responsible for its regularising qualities.
Salle : A707

Séminaire

Séminaire des jeunes chercheurs

Intervenant : DE GENNARO Danièle (CEREMADE)
Titre :
An introduction to Mean Curvature Flows

Le : 3/02/2022 de : 17:00 à : 18:30
Mean Curvature flows are a special case of geometric flows that have attracted lot of interest in a great variety of fields, from Geometry to Physics, passing trough Analysis. In this talk, we will try to give the basic concepts needed to understand the most recent development in this field. In particular, the presentation will be focusing on the definition of sets of finite perimeter and the various notions of weak solution for these flows. If time allows, we will then focus on the topic of volume-preserving Mean Curvature flows.
Salle : A707

Séminaire

Séminaire des jeunes chercheurs

Intervenant : FU Changqing (CEREMADE)
Titre :
Geometry of Image Generation with GANs

Le : 20/01/2022 de : 17:00 à : 18:30
The elements of learning an image consist of: Geometry of shapes, deformation of image features, optimization of Neural Networks, and evaluation of the optimization goals. In this talk, we review the mathematical foundation of these aspects. On top of Deep Learning, Generative Adversarial Network (GAN) is to introduce a posterior counterpart network which fits a function of likelihood to evaluate the optimization goal. Within Neural Networks, Convolution and Transformer add prior structures to the function space that decomposes an image. Along the layers, flow of features follow geometrical regularity. Applications in image manipulation problem is presented
Salle : A707

Séminaire

Séminaire des jeunes chercheurs

Intervenant : EICHINGER Katharina ()
Titre :
An introduction to optimal transport

Le : 13/01/2022 de : 17:00 à : 18:00
In this talk I will introduce the optimal transport problem. Initially introduced as an economic problem to transport certain quantities in an optimal way, it has become very popular in the past decades due to its variety of applications in physics, economics, and data science. After getting accustomed to this problem, I will prove the equivalence to its dual formulation - a tool very useful in convex optimization, and exploit it to prove some standard results. To conclude I will try to give some details of possible applications both of theoretical and practical nature.
Salle : A707

Séminaire

Séminaire des jeunes chercheurs

Intervenant : KOUANDE Adechola ()
Titre :
Phase Transition in the Peierls model for polyacetylene
IMPORTANT: Talk is going to be in French!
Le : 16/12/2021 de : 17:00 à : 18:30
At null temperature, it is a well-known fact that in closed polyacetylene molecular chains having an even number (L = 2N) of carbon atoms (e.g. benzene), the valence electrons arranged themselves one link in two. This phenomenon is well understood in the Peierls model, introduced in 1930, which is a simple non-linear functional describing polyacetylene chains. In this model, there is a break of symmetry, called Peierls instability: the minimizers are never 1-periodic. Many results regarding this model at null temperature has been obtained, especially in the even case (L = 2N) by Tom Kennedy and Elliott H. Lieb who showed the stability of the Peierls instability and also in the odd case (L = 2N +1) with the works of Mauricio GARCIA ARROYO and Éric SÉRÉ who showed the existence of a kink state, between the two dimerized configurations. In this talk, we will provide the results obtained by studying this model with temperature. More precisely we will consider the Peierls model for polyactetylene in presence of temperature, we will prove the existence of a critical temperature below which the chain is dimerized or kink-like according to its parity, and above which the system is 1-periodic. The chain behaves like an insulator below the critical temperature and like a metal above it. We will characterize the critical temperature in the thermodynamic limit model and study the bifurcation around it.
Salle : A707

Séminaire

Séminaire des jeunes chercheurs

Intervenant : SCARCELLA Donato (CEREMADE)
Titre :
Introduction to KAM theory with some applications to celestial mechanics

Le : 09/12/2021 de : 17:00 à : 18:30
The KAM theory deals with small perturbations of completely integrable Hamiltonian systems. The phase space of an integrable Hamiltonian system is completely foliated by invariant tori on which the flow is periodic or quasi-periodic, being conjugated to a linear flow. The goal of the KAM theory is to prove that, under a sufficiently small Hamiltonian perturbation, most of these invariant tori survive, being just slightly deformed. The main motivation for KAM theory is related to stability questions arising in celestial mechanics which were addressed by astronomers and mathematicians such as Kepler, Newton, Lagrange, Liouville, Delaunay, Weierstrass, and, from a more modern point of view, Poincaré, Birkhoff, Siegel,.. This talk is consecrated to give a very introductory presentation about this theory, trying to avoid all technicalities, and to give a very naive idea of the applications to celestial mechanics
Salle : A707

Séminaire

Séminaire des jeunes chercheurs

Intervenant : FONTE SANCHEZ Claudia (CEREMADE)
Titre :
Harris-Doeblin method to prove convergence to equilibrium

Le : 02/12/2021 de : 17:00 à : 18:30
A problem could be defined as an object and certain questions about it. Then, researchers set a methodology to try to answer these questions. Our object has two important elements: time and a set of rules that governs how certain states develop in this time. For example, we can speak of partial evolution equations describing the time elapsed since the last spike of a neuron. Our questions: Does such a system have a state of equilibrium? an immovable state under this set of rules? And if it exists, is it that given any initial state our system will converge in time to this state of equilibrium? How fast? In this talk we introduce the Doblin-Harris method to answer these questions. In particular, we prove exponential velocity convergence toward the steady state in a simple neuroscience model
Salle : A707

Séminaire

Séminaire des jeunes chercheurs

Intervenant : PETIT Romain (CEREMADE)
Titre :
Variational methods for solving inverse problems, with applications in imaging

Le : 18/11/2021 de : 17:00 à : 18:30
The topic of this talk will be linear inverse problems, which consist in recovering an unknown element of some vector space from the knowledge of its image by a linear map, possibly corrupted by some noise. I will introduce variational methods allowing to achieve this, which consist in producing an approximation of the unknown by solving a carefuly chosen optimization problem. I will focus on the link between the structure the unknown is assumed to have and the design of the variational formulation. Many examples coming from signal processing and statistics will be given. I will also try to show how beautiful questions mixing convex analysis, calculus of variations, and even geometry come out of the wide variety of problems we can model using this framework.
Salle : A707

Séminaire

Séminaire des jeunes chercheurs

Intervenant : HSU Yueh-Sheng (CEREMADE)
Titre :
SPDE and Regularity Structures - Motivations and Ideas

Le : 10/11/2021 de : 17:00 à : 09:00
The aim is to introduce the (singular) SPDEs and to explain why their meaning is often mathematically unclear. Firstly the notion of white noise will be motivated and defined. Secondly several examples of singular SPDEs will be given and we will discuss their ill-posedness, raise the problem of undefined terms involving noise as well as the necessity of renormalisation. Finally, we come to the ideas of regularity structure, which is now regarded as the most robust theory for defining and solving SPDEs. The talk shall be kept in a fairly informal/heuristic tone and is aimed at making clear the principal ideas.
Salle : A707

Séminaire

Séminaire des jeunes chercheurs

Intervenant : CAZALIS Jean (CEREMADE)
Titre :
Quantum mechanics and the stability of matter

Le : 04/11/2021 de : 17:00 à : 18:30
The full theory of quantum mechanics started to emerge around 1925-1926 with Heisenberg’s matrix model and Schrödinger’s wave model and constitutes one of the major scientific achievement of the past century (together with Tsar Bomba and mass surveillance). In this introductory course, I will first present the mathematical formalism of quantum mechanics, giving the main physical motivations behind it. After that, I will investigate one of the early success of quantum mechanics: the stability of the hydrogen atom. Then, if time permits, I will present general atomic models, explaining why and how to construct approximation methods. In sake of inclusiveness, the level of technicality will remain as low as possible. In particular, you will not hear about Sobolev spaces during this talk, I promise
Salle : A707

Séminaire

Séminaire des jeunes chercheurs

Intervenant : ALVAREZ Frank (CEREMADE)
Titre :
Evolution of a structured cell population endowed with plasticity of traits under constraints on and between the traits

Le : 28/10/2021 de : 17:00 à : 18:30
Confronted with the biological problem of managing plasticity in cell populations, which is in particular responsible for transient and reversible drug resistance in cancer, we propose a rationale consisting of an integro-differential and a reaction-advection-diffusion equation, the properties of which are studied theoretically and numerically. By using a constructive finite volume method, we show the existence and uniqueness of a weak solution and illustrate by numerical approximations and their simulations the capacity of the model to exhibit divergence of traits. This feature may be theoretically interpreted as describing a physiological step towards multicellularity in animal evolution and, closer to present-day clinical challenges in oncology, as a possible representation of bet hedging in cancer cell populations
Salle : A707

Séminaire

Séminaire des jeunes chercheurs

Intervenant : KELLY Luke (CEREMADE)
Titre :
Phylogenetics

Le : 25/10/2021 de : 17:00 à : 09:00
Phylogenetics the problem of reconstructing the ancestry of a set of taxa. The phylogeny is typically a tree whereby the leave nodes are the observed taxa, edges represent evolving species, and internal nodes denote speciation events. Phylogenetic methods are frequently applied in the life sciences; we might be interested in inferring the origin time of an infectious disease and have samples on hundreds or thousands of taxa, for example. Fitting a phylogenetic model is a difficult statistical problem: we jointly attempt to infer a dated tree (topology and branch lengths), parameters of the evolutionary process on the tree, and other variables of interest; the likelihood is given by an integral over a tree; we only observe data at the leaves of the tree; and assessing model fit is extremely difficult. Markov chain Monte Carlo methods are the primary tool for Bayesian phylogenetic inference, but it is challenging to construct efficient schemes to explore the associated posterior distribution and to then assess their convergence. In this talk, I will introduce the problem of phylogenetic inference and illustrate it on a problem in historical linguistics. I will describe a method developed during my DPhil to infer phylogenetic trees when traits may also be acquired outside of ancestral relationships and the computational cost of the likelihood calculation grows exponentially in the number of taxa. Recent work uses couplings of Markov chains to diagnose convergence of MCMC samplers. In the second half of the talk, I will describe how to construct couplings of Markov transition kernels on trees and other phylogenetic model components and use them to efficiently diagnose convergence in this setting.
Salle : A707

Séminaire

Séminaire des jeunes chercheurs

Intervenant : REGE Alexandre (Laboratoire Jacques-Louis Lions)
Titre :
Applying spectral theory to the study of the Bernstein-Landau paradox

Le : 26/11/2020 de : 17:00 à : 18:00

Salle : En ligne

Séminaire

Séminaire des jeunes chercheurs

Intervenant : SIMONOV Nikita ()
Titre :
A conversation about functional inequalities

Le : 24/09/2020 de : 17:15 à : 18:15
Functional inequalities play a key role in problems arising in the calculus of variations, partial differential equations, and geometry. In this talk, we will discuss some fundamental examples of functional inequalities. Our focus will be mainly on Sobolev and Gagliardo-Nirenberg inequalities. Lastly, we will address the question of "stability" and discuss some recent results obtained in collaboration with M. Bonforte, J. Dolbeault, and B. Nazaret
Salle : P510

Séminaire

Séminaire des jeunes chercheurs

Intervenant : FLORIO Anna (IMJ-PRG)
Titre :
Une introduction à la théorie KAM faible

Le : 26/03/2020 de : 17:00 à : 18:00

Salle : A711

Séminaire

Séminaire des jeunes chercheurs

Intervenant : BARBIERI Santiago (Université Paris-Sud)
Titre :
On the mathematical stability of the Sun-Jupiter-Saturn system

Le : 12/03/2020 de : 17:00 à : 18:00

Salle : P507

Séminaire

Séminaire des jeunes chercheurs

Intervenant : BOURSIER Jeanne (CEREMADE)
Titre :
Some aspects of the statistical physics of Coulomb gases

Le : 13/02/2020 de : 00:00 à : 00:00

Salle : P507

Séminaire

Séminaire des jeunes chercheurs

Intervenant : BOURSIER Jeanne (CEREMADE)
Titre :
Some aspects of the statistical physics of Coulomb gases

Le : 13/02/2020 de : 17:00 à : 18:00

Salle : P507

Séminaire

Séminaire des jeunes chercheurs

Intervenant : BRIGATI Giovanni (Université Paris-Dauphine)
Titre :
AN INTRODUCTION TO CALCULUS AND GEOMETRY IN METRIC SPACES

Le : 12/12/2019 de : 17:00 à : 18:00

Salle : P507

Séminaire

Séminaire des jeunes chercheurs

Intervenant : LIU Yating (LPSM)
Titre :
Optimal quantization : Limit Theorems, Clustering and Simulation of the McKean-Vlasov Equation

Le : 28/11/2019 de : 17:00 à : 18:00
The presentation contains two parts. The first part addresses two limit theorems related to optimal quantization: (i) the characterization of the convergence in the Wasserstein distance of probability measures by the pointwise convergence of Lp-quantization error functions and (ii) the convergence rate of the optimal quantizer and the quantization performance for a probability measure sequence converging in the Wasserstein distance, especially for the empirical measures. The second part is the application of the optimal quantization method in the simulation of the McKean-Vlasov equation dXt = b(t, Xt, ?t)dt + ?(t, Xt, ?t)dBt.
Salle : P324

Séminaire

Séminaire des jeunes chercheurs

Intervenant : PETIT Quentin (CEREMADE)
Titre :
A mean-field game approach to price formation in ressources markets

Le : 14/11/2019 de : 17:00 à : 18:00
In this work, we present a growth model to understand how the prices of certain resources useful for production are set. We consider a large number of small players with the ability to produce using "limited" resources. Our model is an example of a mean-field game where the interaction is at the price level. We establish the existence of solutions by using a fixed point method.
Salle : P507

Séminaire

Séminaire des jeunes chercheurs

Intervenant : TRIAY Arnaud (CEREMADE)
Titre :
Dynamics of a Bose gas

Le : 23/05/2019 de : 17:00 à : 18:00
Bose-Einstein condensation is a phenomenon happening at very low temperature where a dilute gas of bosonic particles macroscopically occupy the same quantum state. In this regime, instead of dealing with a N particle system, one can effectively describe the system by a simple equation, the Gross-Pitaevskii equation. This talk is about the mathematical derivation of this one-particle model with emphasis on the time-evolution. We will recall the second quantization formalism (Fock space) and use it to give a sketch of proof.
Salle : A707

Séminaire

Séminaire des jeunes chercheurs

Intervenant : AFFILI Elisa (EHESS & Università degli studi di Milano)
Titre :
Scalar Wars: A New Lotka-Volterra Competitive System

Le : 11/04/2019 de : 17:00 à : 18:00
Imagine a territory where two (human) populations live together in competition. What happens if one of the two wants to get rid of the other and attacks it? And what are the differences if, instead of living together, the two populations inhabit two neighbouring territories? In this talk we will discuss some non-variational models for two populations at war. These results were done in collaboration with Serena Dipierro, Luca Rossi, and Enrico Valdinoci.
Salle : A707

Séminaire

Séminaire des jeunes chercheurs

Intervenant : FERRé Grégoire (CERMICS)
Titre :
Some gentle ergodicity results

Le : 28/02/2019 de : 17:00 à : 18:00
Studying the long time behaviour of Markov chains is an important theoretical and practical problem. Indeed, it may be used to assess the validity of physical models such as particle systems or stochastic PDEs, as well as to control discretization schemes and their rates of convergence for Monte Carlo methods, a standard problem in statistics and Machine Learning. Such convergence results are generally referred to as "ergodicity". The same issues arise concerning the so-called Feynman--Kac dynamics, which are used both for rare event analysis and eigenvalue estimation. This latter dynamics corresponds in practice to a Markov chain with an additional genealogical feature. The goal of the talk is to provide a gentle introduction to these problematics. I will start by considering the ergodicity of Markov chains on a bounded domain, detailing a very elegant and short proof by M. Hairer. This will be a good starting point to explain the more general result of Hairer and Mattingly (2011). In a second time, I will present the problematic of Feynman-Kac dynamics, whose study is made difficult because of a nonlinear effect. If time allows, I'll explain how to cast this nonlinear problem into the linear framework of Hairer and Mattingly [G.F., G. Stoltz, M. Rousset, 2018].
Salle : A707

Séminaire

Séminaire des jeunes chercheurs

Intervenant : ZHANG Christophe (LJLL, Sorbonne Université)
Titre :
Internal rapid stabilization by a scalar feedback for the 1-D linear transport equation

Le : 31/01/2019 de : 17:00 à : 18:00
We use the backstepping method to study the stabilization of a 1-D linear transport equation by controlling the scalar amplitude of a piecewise regular function of the space variable in the source term with a linear feedback control. The backstepping method consists in mapping the system into another target system, which is known to be stable. The feedback then becomes a parameter of this backstepping transformation, and the stabilization problem consists in finding parameters for which this transformation is invertible. Initially designed in the case of boundary controlled systems, using Volterra transforms of the second kind, the method has been extended to systems with internal control, and to more general transformations of the Fredholm form. Using this method, we prove that when the system is exactly controllable, then it can be exponentially stabilized by means of a linear feedback. For a given decay rate, we give an explicit feedback that achieves that decay rate. From these explicit feedback laws, we then derive an explicit stationary feedback law that achieves finite-time stabilization.
Salle : A304

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Séminaire des jeunes chercheurs

Intervenant : GARREC Tristan (CEREMADE)
Titre :
Communicating Zero-Sum Product Stochastic Games

Le : 08/11/2018 de : 17:00 à : 18:00
We present two classes of zero-sum stochastic games. These two classes assume a communication property on the state spaces of the players. For strongly communicating on one side games, we prove the existence of the uniform value. For weakly communicating on both sides games, we prove that the asymptotic value, and therefore the uniform value, may fail to exist.
Salle : A707

Séminaire

Séminaire des jeunes chercheurs

Intervenant : MARCHAND Pierre (INRIA & LJLL)
Titre :
Équations intégrales de frontière et de méthodes de décomposition de domaine

Le : 25/10/2018 de : 17:00 à : 18:00
Les équations intégrales de frontière sont une reformulation d’équations aux dérivées partielles à l’aide d’opérateurs intégraux non-locaux. Elles ont l’avantage de n’être posées que sur la frontière du domaine considéré, ce qui permet de diminuer d’une dimension la géométrie du domaine à discrétiser et de pouvoir résoudre naturellement des problèmes ouverts. Ce type de reformulation est par exemple utilisé en acoustique, en électro-magnétisme ou en mécanique. Après discrétisation de ces équations intégrales, les matrices obtenues ont l’inconvénient d’être pleines du fait des opérateurs intégraux non-locaux, ce qui nous amène à vouloir utiliser des méthodes de résolution itératives comme le gradient conjugué ou GMRes pour résoudre les systèmes linéaires associés. Pour stabiliser le nombre d’itérations de ces solvers linéaires vis à vis de la finesse de discrétisation, une solution usuelle est d’utiliser un préconditionneur. Dans cet exposé, après avoir introduit les équations intégrales de frontière, nous présenterons une méthode pour préconditionner de telles matrices issues de la décomposition de domaine, ainsi que son analyse. Ces travaux ont été effectués en collaboration avec Xavier Claeys et Frédéric Nataf.
Salle : A711

Séminaire

Séminaire des jeunes chercheurs

Intervenant : PAGNARD Camille (CEREMADE)
Titre :
Limites locales et profils de grands arbres Markov branchants
Présentation des travaux de thèse
Le : 10/10/2018 de : 17:00 à : 18:00
Dans cet exposé, je présenterai mes travaux de thèse qui portent sur les propriétés asymptotiques de modèles d'arbres aléatoires satisfaisant la propriété dite de Markov branchante. En particulier, nous établirons un résultat de convergence de ces arbres au sens de la limite locale vers des arbres infinis qui satisfont une version de cette même propriété de Markov branchante. Nous donnerons de plus un résultat sur la convergence au sens des limites d'échelle pour cette famille d'arbres infinis. Nous nous intéresserons ensuite au comportement asymptotique du profile des arbres Markov branchants finis ainsi qu'à la régularité du profil limite.
Salle : A711

Séminaire

Séminaire Séminaire des jeunes chercheurs

Intervenant : BRUNED Yvain (LPMA)
Titre :

Le : 28/03/2014 de : 16:30 à : 17:30

Salle :

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Séminaire Séminaire des jeunes chercheurs

Intervenant : HAJEJ Ahmed ()
Titre :

Le : 14/03/2014 de : 16:30 à : 17:30

Salle :

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Séminaire Séminaire des jeunes chercheurs

Intervenant : DUMITRESCU Roxana ()
Titre :

Le : 07/03/2014 de : 16:30 à : 17:30

Salle :

Séminaire

Séminaire Séminaire des jeunes chercheurs

Intervenant : LAGUZET Laetitia (CEREMADE)
Titre :
Optimal vaccination policies as Mean Field Games equilibriums / A numerical algorithm for fully nonlinear HJB equations

Le : 14/02/2014 de : 16:30 à : 17:30

Salle : A 403

Séminaire

Séminaire Séminaire des jeunes chercheurs

Intervenant : OLIVIER Adélaïde (CEREMADE)
Titre :
Nonparametric estimation of the jump rate of a piecewise deterministic Markov process: an aged-structured model on a tree

Le : 31/01/2014 de : 16:30 à : 17:30

Salle : A403

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