Lambda Seminars #

The Lambda seminar meets approximately once every two weeks, and its main objectives are to

• allow doctoral students to present both their research topic and any other topic they like, and to do so in a relaxed and probably less stressful environment than that of a first major conference.
• allow doctoral students in the audience to find out what their colleagues are doing, so that fruitful discussions and collaborations are not missed.
• to allow everyone more broadly to enrich their culture about « what is currently being done » in mathematics.

An introduction to Isogeny-based cryptography

December 20, 2023 / 17:15 # DARTOIS Pierrick (Université de Bordeaux-IMB)

↕

In 1995, Peter Shor proved that a quantum computer with enough capabilities could factor integers and solve discrete logarithms in polynomial time. This would be a major threat to all public key cryptographic protocols relying on RSA and elliptic curves discrete logarithms that we use nowadays. Over the last decade, the cryptography community started to propose post-quantum protocols resilient to these attacks. Isogenies between elliptic curves (and higher dimensional abelian varieties) could be part of the solution. This talk will introduce isogeny-based cryptography. We shall see the basic mathematical concepts of isogenies, the key exchange protocol SIDH (supersingular isogeny Diffie-Hellman) and recent attacks breaking it with the help of isogenies in higher dimension. Finally, we shall briefly see how these attacks can be used to build new protocols.

Center-outward ordering of scatter plots.

November 22, 2023 / 17:15 # THURIN Gauthier (Université de Bordeaux-IMB)

↕

All attempts to generalize univariate quantiles to the multidimensional framework (d>1) face the same problem: the absence of a canonical order relationship.

Yet quantiles on the real line are the basis of many applications, including statistical tests, quantile regression, uncertainty quantification, risk analysis, etc.

The sticking point, apart from choosing how to order the random observations of a scatter plot, lies in the properties expected to enable the said applications. A recent concept, defined through the theory of optimal transport, combines all the properties that make the univariate quantile function so successful.

The presentation will provide an overview of these properties and of the applications that have emerged in the literature in recent years.

Mathematical Study of a Mixture of Polyatomic Gases

October 18, 2023 / 17:00 # SHAHINE Marwa (Université de Bordeaux-IMB)

↕

In this talk, a detailed explanation of the mathematical study of gases will be presented. We will consider the Boltzmann equation that models a mixture of polyatomic gases by representing the internal energy by a continuous parameter. Under some convenient assumptions on the collision cross-section, we prove that the linearized Boltzmann operator L is a Fredholm operator. For this, we write L as a perturbation of the collision frequency multiplication operator. We prove that the collision frequency is coercive and that the perturbation operator is Hilbert-Schmidt integral operator. This result is essential for proving the existence of a solution to the Boltzmann equation, and for deriving macroscopic equations (Navier-Stokes,..) starting from the Boltzmann equation.

Deep Learning for Brain Tumor Segmentation

September 27, 2023 / 16:30 # DESIER Kylian (Université de Bordeaux-IMB)

↕

Artificial Intelligence is definitely hot topic lately. You probably heard tons of people praising AI and its possibilities while others warn about all the misuse it can lead to. Taking the specific case of Brain Tumor segmentation, I hope to highlight that some applications might be good by explaining how it can help clinicians, what are the different challenges encountered and rapidly explain how it works.

Image restoration with deep generative models

June 7, 2023 / 16:30 # PROST Jean (Université de Bordeaux-IMB)

↕

Image restoration problems, such as deblurring, inpainting or super-resolution, can be formulated as inverse-problems, where the goal is to recover the clean signal from its degraded observation.Those inverse problems are typically ill-posed, and it is therefore necessary to introduce some form of regularization to produce a satisfying solution. In a Bayesian framework, the regularization is related to the prior distribution of the natural images.

In this talk, I will present how we can use recent deep generative models (DGM) as a prior to regularize image inverse problems. DGM provide a strong prior on natural images, but using them to regularize inverse problem is a difficult task because of their complex architecture. I will present a new algorithm based on alternate optimization, which exploits variational autoencoders, a specific instance of DGM. I will show how this method can solve image inverse problems efficiently, while providing theoretical convergence guarantees under reasonable assumptions.

Petit catalogue des différents modes de convexités

May 17, 2023 / 16:30 # DELANDE Loïs (Université de Bordeaux-IMB)

↕

You’re probably familiar with convex functions, but do you know what a strongly convex function is? And a quasiconvex function? If so, well done to you (: otherwise it doesn’t matter, I forgive you, but come and discover this universe, which is more complex than you suspect, with notions each stranger than the other, but always with an underlying motivation. (well it seems to me).

Numerical Modelling of Wave Energy Converter Farms

May 10, 2023 / 15:15 # BATTISTI Beatrice (Université de Bordeaux-IMB)

↕

As the demand for renewable energy resources becomes urgent in the energy sector, wave energy plays a key role because of its untapped potentiality. Different kinds of Wave Energy Converter (WEC) at different levels of technology readiness are being developed to extract energy from waves. They all have in common their deployment in farms, as an essential step for wave energy to reach commercial scale and be comparable to other renewable energy sources. Numerical simulations of WEC farms are a necessary step before installation in real sea sites, but are also computationally expensive. Motivated by the intrinsic necessity of high-fidelity, yet computationally efficient, dynamical models for WEC farms, a versatile multi-fidelity model based on domain decomposition is presented, coupling a CFD solver for the near-field, in the vicinity of the WEC, and a lower fidelity solver based on Model Order Reduction for the far-field.

Compact Riemann surfaces

April 26, 2023 / 16:30 # GUNNING Dean (Scotland)

↕

Compact Riemann surfaces are compact 2-manifolds that locally look like the complex plane. Not only do such surfaces guarantee a conformal structure, but these surfaces can be identified with complex projective curves and give rise to important results central to complex geometry, such as the Riemann-Roch theorem. We give an introduction to these structures, as well as their broader applications.

An introduction to the Nagell-Ljunggren equation

April 5, 2023 / 16:30 # CHEN Han (University of Gottingen)

↕

The Diophantine equation of Nagell-Ljunggren $\frac{x^{n}-1}{x-1}=y^{q}$ has six known solutions in integers with exponents larger than one. It is conjectured that these are the only solutions. In this talk, I will briefly introduce the history of N-L equation and its connection with the famous equation of Catalan. I will also show some results under the condition that $q$ does not divide $h_p^-$, the minus part of the class number.

Méthode numérique pour la Tomographie par Impédance Électrique.

March 29, 2023 / 16:31 # NASR Niami (Inria)

↕

Electrical impedance tomography (EIT) is a non-invasive technique for reconstructing conductivities from electrical measurements at the surface of the body. An alternating current is injected through several electrodes and electrical potential measurements are taken. To numerically solve the inverse problem associated with the EIT, we use a numerical method of immersed boundary. We will discuss the following two points: What exactly is this inverse problem? What is the submerged boundary method?

Binomial Cayley Graphs and Applications to Dynamics of Finite Spaces

March 15, 2023 / 16:30 # VIGANO Francesco (Imperial College London)

↕

This talk is about binomial Cayley graphs. Cayley graphs are graphs on groups (with extra conditions). The edge weight function of a Cayley graph induces new weight functions, obtained by considering the binomial coefficient of the original weight function and a natural number. We refer to graphs arising from this construction as binomial Cayley graphs. We will present two families of binomial Cayley graphs, associated with symmetric groups and powers of cyclic groups. Interesting combinatorial properties arise through the spectral analysis of their adjacency matrices. For example, in the symmetric group case, a relation between the multiplicity of the null eigenvalue and longest increasing sub-sequences of permutations can be obtained through the celebrated RSK correspondence. An application to n-point motion in discrete dynamical systems will be presented.

A brief introduction to linear model reduction

March 1, 2023 / 16:30 # TIFOUTI Ishak (IMB)

↕

The reduced basis method was specifically developed in the context of parameterized equations. It makes use of the parametric dependency of the solution to build an approximation space of the solutions manifold (“the graph of the parametric mapping”). We will outline the notion of manifold’s “reducibility” by introducing the so-called Kolmogorov n-width and see how to justify our reduction with accurate error estimates.

Etude de Réseaux de neurones à l'aide des Probabilités libres :

February 22, 2023 / 17:00 # DABO Issa (IMB)

↕

Free probability theory aims to study non-commutative random variables and it differs from classical probability by its algebraic construction. This theory turned out to be very useful in the study of random matrices and their spectrum. After a brief introduction to free probability, we will focus on neural networks, which can be built from random matrices, and study them thanks to free probability.

Little dictionary of artificial neural networks

February 8, 2023 / 16:30 # INACIO Éloïse (IMB)

↕

This presentation aims at providing a good starting point for understanding convolutional neural networks. I’ll first give a brief overview of artificial intelligence and artificial neural networks before focusing on 2nd generation neural networks and more specifically, their applications in computer vision. All the vocabulary necessary to understand most articles in the field will be tackled.

Modélisation mathématique et assimilation de données de la dynamique d'une Cellule Tumorale Circulante dans le flux sanguin

January 25, 2023 / 16:30 # GRANET Julien (IMB)

↕

In this presentation, we are interested in the behavior of a tumor cell after it has detached from its original tumor to rejoin the bloodstream. This is then called a circulating tumor cell. Determining its dynamics is fundamental for understanding the distribution of metastases in an organism. Emphasis will be placed on the methods deployed to link the experimental data to the mathematical model. Keywords: mathematics applied to biology, ODE, parameter estimation, fluid mechanics

Cryptography using class groups of quadratic fields

January 11, 2023 / 16:30 # BEAUGRAND Agathe (IMB)

↕

In this talk, I will give an introduction to cryptography based on class groups of quadratic fields, and in particular to the CL encryption scheme. After a brief introduction to asymmetric encryption, I will explain how to construct class groups of quadratic fields for cryptography. Finally I will present the CL encryption scheme and its advantages with respect to other encryption schemes.

Component-based model order reduction procedure for large scales thermo-hydro-mechanical systems.

December 7, 2022 / 16:30 # SAMBATARO Giulia (IMB)

↕

This talk is about a new component-based model order reduction procedure for a class of problems in nonlinear mechanics with internal variables. The work is motivated by applications to thermo-hydro-mechanical (THM) systems for radioactive waste disposal (this project is funded by ANDRA, the national agency for radioactive waste management). Keywords: model order reduction, domain decomposition, nonlinear elasticity, coupled problems.

Introduction to interpolation and random interpolation in spaces of holomorphic functions.

November 16, 2022 / 16:30 # LAMBERTI Giuseppe (IMB)

↕

The talk will be an introduction to interpolation problems in spaces of holormophic functions of one variable. I will start from the original problem, stated for bounded holomorphic functions in the unit disk, to then introduce it for reproducing kernel Hilbert spaces. The last part will be about random interpolation, in particular I will focus on Steinhaus sequences.

Résolution et propriétés qualitatives de quelques EDP: Du linéaire au non-linéaire.

November 9, 2022 / 16:30 # TENDANI-SOLER Adrien (IMB)

↕

The talk will focus on three partial differential equations: the heat equation, the wave equation, and the Schrödinger equation. First, I will expose some mathematical properties of these equations as well as their conceptual implications. Finally, we will look at the nonlinear version of these equations, the methods involved and the link with the initial linear equation.

Wasserstein Multivariate Autoregressive Models for distributional time series and its application in graph learning

October 26, 2022 / 17:00 # JIANG Yiye (IMB)

↕

In this work, we propose a new autoregressive model for multivariate distributional time series. We consider a collection of N series of distributions defined over a bounded interval in R, which are indexed by distinct time instants. Especially, we wish to develop such a model which can identify the dependency structure in the temporal evolution of the measures. To this end, we extend the classical vector autoregressive model X_t = AX_{t-1} + Z_t, for t in Z, which resides in R^N to a model in Wasserstein space W_2(R) which is a metric space of univariate distributions whose 2nd moments exist, endowed with the L2-distance between their quantile functions. The model coefficients parametrize the dependency structure. We show that the proposed model is a theoretical valid time series model. In particular, we propose a method to estimate the model coefficient from a finite number of observations. We fit the proposed model on two real data sets: age distribution of countries and the bike sharing network in Paris. We visualize the corresponding estimated dependency structures on the real geographical maps, which demonstrate the effectiveness of the proposed model.

Caractère discret du groupe de torsion d'une variété abélienne sur un corps local.

October 12, 2022 / 16:30 # SALIGUE Lilian (IMB)

↕

The group of torsion points is a central element in the study of elliptic curves and abelian manifolds. We will see in this talk a comment on will be able to extend a theorem of Mattuck of 1955 affirming that the torsion group of an abelian manifold on a local field of non-archimedean characteristic 0 is discrete by the same result by removing the hypothesis of zero characteristic. For this we will first give a general overview of all the elements that we will use before defining a distance and an associated topology. We can then suggest our result and explain why this is necessary in our work on the conjecture of Tate and Voloch (1996) which we will also explain.

Kameda Toyojiro and the transfer of the Western theory of probability to Japan at the beginning of the 20th century

June 1, 2022 / 16:30 # LAURENS Clémentine (ESJ Lille)

↕

We will talk about the Japanese actuary and probabilist Kameda Toyojiro (1885-1944) who took a major part in the transfer of modern probabilistic technology to Japan at the beginning of the 20th century. Very familiar with contemporary English and German works, he made an early use of certain fundamental concepts of probability theory, such as characteristic functions, and was one of those who paved the way for the spectacular development of the Japanese probabilistic school in the next generation.

An Introduction to the Wasserstein distance in Statistics

May 3, 2022 / 16:30 # FREULON Paul (IMB)

↕

n this talk, I will give an introduction to the Wasserstein distance and its use in statistics. In a first part, I will present a bio-statistical application that will motivate the need to compare probability distributions. In a second part, I will introduce the Wasserstein distance with some historical elements. For instance, I plan to talk about Monge problem formulated in 1781, Kantorovich contributions in the 1940és, and why statisticians have currently a lot of interest for this distance. In a third part, I will present some explicit formulations of the Wasserstein distance and a few properties of this distance. Finally, I will try to give some statistical results related to this distance. For instance, given samples from two distributions $\mu$ and $\u$ how can we estimate the Wasserstein distance between those two distributions?

Brief introduction to linear forms in logarithm

April 20, 2022 / 16:30 # HONG Haojie (IMB)

↕

An expression of the form $\beta_1\log\alpha_1+\cdots+\beta_n\log\alpha_n$ is called linear form in logarithms, where $\alpha_i$ are given non-zero algebraic numbers and $\beta_j$ are variables. Alan Baker proved that if the $\log\alpha_i$ are linearly independent over the rationals, they are also linearly independent over the algebraic numbers. In this talk, I will give a concise historical introduction to the theory of linear forms in logarithms, then show some main theorems and simple applications.

Deux problèmes d'intersections improbables

April 15, 2022 / 16:30 # TRON Emanuele (IMB)

↕

Improbable intersections are a formalism that groups geometric intersection problems into families with a distinctly arithmetic character. In this talk, we are interested in two of these problems which play an important role in the theory: the conjecture of André-Oort, concerning the points CM in the submanifolds and the equidistribution of Galois, and the conjecture of ‘Ailon-Rudnick, related to heights on bursts and conjectures of Vojta. These two conjectures (and methods for attacking them) touch on topics such as transcendence theory, model theory, subspace theorem, arithmetic intersection theory.

Problème de Plateau et surfaces minimales

March 30, 2022 / 16:30 # MARTINO Dorian (IMJ)

↕

How to find a surface minimizing the area among a given family of surfaces. This problem was first posed by Lagrange in 1760, then was popularized by Plateau during the 19th century by studying soap bubbles and surface tensions. In 1930, Douglas and Rado were the first to propose a general approach to this problem by generalizing the notion of the shortest path between two points. Douglas was awarded one of the first Fields Medals for this work in 1936. In the 1990s, Hélein came up with the idea of using the notion of moving benchmarks which simplified the study of the regularity of solutions. This allows us to really think of them as surfaces and to study them as such. In this talk I will talk about the existence and regularity of minimal surfaces, I will give an idea of how to construct them, and if time allows, I will give some generalizations.

Complete integrability for the KdV equation

March 23, 2022 / 16:30 # NOISETTE Florent (IMB)

↕

The aim of the talk is to discuss the historic paper of Peter Lax where he first introduced the concept of complete integrability. The idea is twofold. Firstly, whenever there exist infinitely many conserved quantities for a given evolution equation, then its solitons interact nicely. Secondly, whenever there exists two conservation laws verifying some conditions for a given evolution equation, there exist an algorithmic procedure to compute infinitely many conservation laws for this equation.

Classical authentification in Quantum Key Distribution

March 11, 2022 / 16:30 # STOCCO Francesco (IMB)

↕

After a brief introduction to cryptography, we will focus on the need for authentication which is the obvious requirement that prevents fraudulent incoming messages to be accepted as genuine. This topic will be discussed also in the context of Quantum Key Distribution (QKD), which is an innovative technology aiming to realize a cryptographic key exchange based on quantum physics laws. QKD has become so important in recent years since it represents a possible solution to the threat of quantum computers against most used current cryptographic schemes.

Vitesse de propagation infinie et contrôlabilité pour l'équation de Schrodinger : le cas du tore

March 2, 2022 / 16:30 # TENDANI-SOLER Adrien (IMB)

↕

Initially, we will be interested in the regularizing effects of the Schrodinger equation and we will make the link with the phenomenon of propagation at infinite speed associated with the Schrodinger equation on the torus. We will then talk about the exact controllability of the Schrodinger equation, which for the torus is verified at any strictly positive time without geometric control condition (CCG) on the observation open. Time permitting, we will consider the need for GCCs for certain fractional Schrodinger equations.

Modules d'Anderson et leurs fonctions $L$-équivariantes

February 9, 2022 / 16:30 # BEAUMONT Tiphaine (IMB)

↕

Soit $K$ un corps global de caractéristique positive et $E-O_K$ un module d’Anderson. Soit $L-K$ une extension abélienne. Nous présenterons une formule de classes équivariante reliant le régulateur équivariant des unités de Stark pour $E-O_L$ é certaines valeurs spéciales de fonctions équivariantes.

The MIT bag model

January 12, 2022 / 16:30 # BENHELLAL Badreddine (IMB)

↕

In this talk, we discuss the Dirac operator on a bounded domain, with the boundary condition called “MIT bag”. After having motivated the study of such an object, I explained how this model appears as the limit (in the sense of the resolvent) of a free Dirac operator (defined on all space) plus a constant potential supported é the outside of.

Couplages de mouvements browniens sur $R^n$ et applications

December 15, 2021 / 16:30 # BENEFICE Magalie (IMB)

↕

The construction of couplings on varieties is a tool allowing to obtain many results whether in probability or in analysis. In particular, Brownian motion couplings provide gradient estimates for the heat semigroup and Poincaré and Sobolev type inequalities. In this talk, I will recall some basic notions about Brownian motion. I will define and detail some pairings on $R^n$, notably so-called co-adapted pairings. Finally, I will present some ideas to extend these couplings to other varieties and I will give an overview of the results that can be obtained with this tool.

Pétrissage par un boulanger mathématicien en théorie du chaos

December 11, 2021 / 16:30 # MEDDANE Antoine (LMJL, Nantes)

↕

Mathematical chaos generally designates an evolutionary behavior (solution of an ODE) which strongly depends on its initial conditions. Hyperbolic dynamics is a special case of chaotic dynamics that has been extensively studied and is still relevant today. In the 1960s and 1970s, S. Smale contributed enormously to the study of these dynamics and notably defined his famous horseshoe which is also known as the baker’s application. In this talk, I will present this application as well as other famous hyperbolic dynamics and then I will discuss mixture for these dynamics.

Introduction to essential dimension

November 24, 2021 / 16:30 # GOUTHIER Bianca (IMB)

↕

de manière équivalente, la dimension essentielle de Sn calcule le nombre de paramètres nécessaires pour écrire un polynôme générateur pour des extensions de corps séparables de degré n. C’est toujours un problème ouvert pour n ?8. Étonnamment

Model Theory of the Complex Exponential Function

November 10, 2021 / 16:30 # GALLINARO Francesco Paolo (University of Leeds)

↕

It is a well-known fact in model theory that subsets of the complex numbers that are definable in the language of rings (so, using polynomials) are either finite or cofinite. In the 1990s, some people started wondering what happens if you add the exponential to the mix: can we say anything meaningful about the subsets of the complex numbers definable using polynomials and exponentials? This question ended up having surprising ties to number theory and complex algebraic geometry. In this talk, I’ll introduce the topic and present some of these connections, focusing on the role of finding solutions to exponential-polynomial equations.

équation aux dérivées partielles et traitement d'image radar marin

October 27, 2021 / 16:30 # MICHELET Jordan (Université de La Rochelle)

↕

Dans cette intervention, il sera présenté des méthodes de traitement d’image basées sur la résolution d’équation aux dérivées partielles. Dans l’objectif de débruiter les images radar marin, il sera présenté deux méthodes dont leur schéma numérique découle de la méthode de Boltzmann sur réseau (en deux dimensions et en temps de relaxation multiple : MRT). Dans un cadre général, il décrit ce schéma numérique qui est très peu utilisé en traitement d’image dans le cas MRT 1, 2, 3. Ensuite, il sera détaillé le lien entre les deux méthodes de traitement d’image et le schéma numérique. Enfin, les contributions 2, 4 et les résultats seront détaillés.1 D. d’Humières, Generalized lattice-Boltzmann equations, in Rarefied Gas Dynamics: Theory and Simulations, vol. 159, pp. 450-458, AIAA Progress in Aeronautics and Astronautics, 1992.2 J. Michelet, M. M. Tekitek et M. Berthier, Multiple relaxation-time lattice Boltzmann model for advection-diffusion equations with application to radar image processing. Soumis dans SIAM Numerical Analysis, 2021.3 K. L. Nguyen, M. M. Tekitek, P. Delachartre et M. Berthier, Multiple relaxation time lattice Boltzmann models for multigrid phase-field segmentation of tumors in 3Dultrason images, SIAM Journal on Imaging Sciences, vol. 12, pp. 1324-1346, jan 2019.4 J. Michelet, L. Mascarilla, H. Chandran et M. Berthier, Geometric segmentation of seaclutter in cohérent radar images: Range-Doppler Map versus Range-Time Intensity Map,IEEE Transactions on Systèmes aérospatiaux et électroniques, vol. 57, p. 2278-2287, 2 août

Condensed Mathematics: exploring a rising theory

October 13, 2021 / 16:30 # ARTUSA Marco (IMB)

↕

Topological spaces are a key concept in modern mathematics, and they can model different types of objects, but not without problemséCondensed Mathematics is a new theory currently being developed by Dustin Clausen and Peter Scholze with the goal of solving such problems by redefining the concept of topological space. The result unifies different branches of mathematics (analysis, p-adic geometry, complex geometry): in this talk, I will present the foundations and the basic definitions of this rising theory. Finally, I will show how Condensed Mathematics can provide a new approach to the classical problem of computing the K-theory of C. In the same way, it is likely that the new objects coming from the condensed world will make it possible to attack mathematical conjectures in a new way.

When quadratic forms enable to derive information about ideals

October 1, 2021 / 16:30 # DALLAPORTA William (IMT)

↕

In 1847 Gabriel Lamé published an incorrect proof for the Theorem of Fermat-Wiles. It has not a lot to do with the heart of this presentation where quadratic forms will play a leading role. The author invites you first to rediscover the introduction of the ideal class group difficult to control but having lot of arithmetic information then to relive the experiments he made thanks to the link (in the quadratic case) between this group and the quadratic forms regarding a problem of specialization of ideals in integral values.“Quand les formes quadratiques permettent l’étude d’idéaux

Introduction to the Stochastic Sakharov system

June 17, 2021 / 16:30 # BARRUÉ Grégoire (IRMAR)

↕

The Zakarov system is a simplified model for the description of long-wavelength small-amplitude Langmuir oscillation in a ionized plasma. Langmuir waves are rapid oscillations of the electron density. In our case we study a stochastic version of the Zakharov system, which means a Zakharov system perturbed by a sochastic noise. In this talk, I will try to explain the general study plan for a Partial Differential Equations (PDE), then I will introduce some stochastic tools to show how it is possible to gather deterministic and stochastic theories to solve our problem.

Approximation d'un problème de contrôle optimal sur un réseau

June 10, 2021 / 16:30 # CHUBERRE MERIADEC (INSA Rennes)

↕

An optimal control problem is associated with a dynamical system of the form y’=f(y,a), where the parameter a is a control fixed by the operator and at a cost that we seek to minimize. Bellman’s approach is to study the value function of the problem. This is the viscosity solution of a Hamilton-Jacobi-Bellman equation. Since 2013, a theory of H-J equations posed on a lattice has been developed (Achdou-Camilli-Cutri-Tchou and Imbert-Monneau-Zidani), precisely associated with a dynamical system evolving on this structure. In this talk I will talk about the theory of viscosity solutions and Hamilton Jacobi’s equations, and I will present the work I am doing in my thesis, which consists of trying to approach a control problem on the network from a series of control problems posed on the whole space. More precisely, we start from a dynamic system controlled in the whole plane to which we add a penalization term to bring the solutions towards a network of the plane and we seek the limit problem which should be a control problem posed on the network.

Sommes de caractères et applications en théorie des nombres

May 6, 2021 / 16:30 # UNTRAU Théo (IMB)

↕

The purpose of my talk is to explain why sums of characters arise naturally in number theory. I will start by talking about duality of finite abelian groups, defining the characters, then I will talk more precisely about the case of additive and multiplicative characters modulo n, which play a central role in analytic number theory. The sums of such characters appear in point counting problems on manifolds defined over a finite field, but also in many other questions of number theory. I will present an application of a non-trivial bound on the modulus of Kloosterman sums to a problem of representing integers by a diagonal quadratic form in 4 variables.

Mathematics, beyond publications

April 15, 2021 / 16:30 # Vergara Hermosilla Gaston (IMB)

↕

his talk consists of two moments:In the first one, we will address part of the research results obtained by the speaker during his doctoral thesis, covering works on (analysis and control of) PDEs, (estimation of cases of) COVID-19, (location of roots of) polynomials, and numerical simulations.In the second moment, the intention is to generate a discussion with the participants, covering some of the questions (philosophical and-or ethical) that have arisen or motivated the daily work of the speaker in the course of each of the investigations mentioned above, such as: what kind of math do we do? what kind of math do we want to do? where and for whom do we publish?

Equations de Schrodinger logarithmiques

April 8, 2021 / 16:30 # CHAULEUR Quentin (IRMAR)

↕

After a presentation of the classical techniques used for the study of the usual linear and nonlinear Schrodinger equations, we are interested in a particular nonlinear Schrodinger equation resulting from Bohmian mechanics (deterministic theory of quantum mechanics) presenting two logarithmic non-linearities: study of particular (Gaussian) solutions, local existence of solutions, long-time behavior, numerical behavior, etc. Particular emphasis will be placed on the link between Schrodinger’s equation and quantum fluid mechanics.

Global well-posedness of 3D homogeneous and inhomogeneous MHD system with small unidirectional derivative

January 26, 2021 / 16:30 # AARACH Nacer (IMB)

↕

We present the MHD (magnetohydrodynamic) equations. Those equations describe the motion of several conducting, incompressible and immiscible fluids in presence of a magnetic field. We investigate some methods to get well posedness for this system in Besov spaces. Those methods can tackle the homogenuous as well as the inhomogenuous case.

From polyhedra to operads

October 15, 2020 / 16:30 # POLIAKOVA Dasha (University of Copenhaguen)

↕

I will construct associahedra and multiplihedra - polytopes which are responsible for non-associativity in algebra. I will therefore introduce operads in general and A-infinity operad in particular. If time permits, I will discuss some contractions of associahedra and multiplihedra.

Self-contracted dynamics and extensions

October 8, 2020 / 16:30 # TAPIA SEBASTIAN (IMB)

↕

Self-contracted dynamics were introduced in 2010. This is a metric property which is an abstract framework for several dynamics that come from optimization. The rectifiability of self-contracted curves was the main question about this phenomena, which was established in 2015 for finite dimensional Euclidean spaces and in 2017 for finite dimensional normed spaces. In this talk we present some results concerning self-contracted dynamics, the main ideas of the euclidean technique for rectifiability and we explore different extensions of the self-contracted notion.

Théorèmes HKR en géométrie dérivée.

June 22, 2020 / 16:30 # MONIER Ludovic (Institut de Mathématiques de Toulouse)

↕

After a quick introduction to derived geometry, I will expose the different versions of the HKR theorem, in zero characteristic, and also in any characteristic with the filtered circle. Time permitting, the possibilities of the existence of crystalline or prismatic analogues of this circle will be discussed.

Fonctions L et courses de nombres premiers

March 12, 2020 / 16:30 # BAILLEUL Alexandre (IMB)

↕

The distribution of prime numbers is deeply related to the distribution of the zeros of certain analytic functions, called L-functions. A relatively recent and little-known problem concerning the distribution of prime numbers is that of “prime number races”. The typical example is the following: although the numbers of primes less than x congruent to 1 mod 4 and to 3 mod 4 are asymptotically equivalent when x tends to infinity (prime number theorem in arithmetic progressions), we observe that the first ones congruent to 3 mod 4 appear more frequently than those that are congruent to 1 mod 4. In the talk, I will explain how to study this phenomenon, called Chebyshev’s bias, in various contexts using L-functions.

Some conclusions about a system modelling rigid structures floating in a viscous fluid

February 7, 2020 / 16:30 # Vergara Hermosilla Gaston (IMB)

↕

In this talk we will study a PDE based model for the vertical motion of a solid floating at the free surface of a shallow viscous fluid. We will show that the governing equations define a well-posed linear system, and thanks to an explicit form of the transfer function we prove that system is input-output stable. In the second part of the talk, we will present some recent results about a diffusive representation and the asymptotic behaviour of an equation of Cummins type associated to the PDE model.

Recursive parameters estimation of a cluster of space debris by filtering on Lie groups

January 30, 2020 / 16:30 # LABSIR Samy (IMS/Université de Bordeaux)

↕

This work addresses the problem of tracking a cluster of space debris sufficiently close to each other to be considered as a single extended object. State-of-the-art random-matrix methods estimate the kinematics of the object shape and centroid by assuming that its shape is elliptic and that the observations are randomly distributed within this ellipsoid. However, space debris, whose motion is driven by the gravitational force, spread out into a “banana”-like-shaped cluster. We propose a novel Lie-group based parameterization to intrinsically capture the “banana”-like shape. More precisely, we first formulate the centroid and shape tracking problem as filtering on Lie groups. Then, we derive an iterated extended Kalman filter on Lie groups to perform jointly the shape and centroid estimation of cluster.

Non annulation de fonctions L en la valeur centrale

January 24, 2020 / 16:30 # FROT Robin (Laboratoire Paul Painlevé, Université de Lille)

↕

L-functions, which are defined as analytic extensions of Dirichlet series, play an important role in number theory. We can indeed connect various objects (elliptic curves, automorphic forms, Galois representations) through their function L. The understanding of these functions in the central value (center of symmetry of a functional equation) is essential in many problems. After introducing the notion of L functions, we will see various analytical tools allowing us to conclude that some of them are not cancelled.

Canonical Lift of Genus 2 Curve

January 17, 2020 / 16:30 # MAIGA Abdoulaye (IMB - Cheikh Anta Diop University)

↕

This talk first gives a survey of the p-adic methods that compute the characteristic polynomials of elliptic curves over finite fields. We then present the complexities to extend those algorithms to genus 2 curvesover finite fields : we propose to extend the canonical lift algorithm introduced by T. Satoh to genus 2 curves over finite fields, using themodular polynomials in dimension 2.

Etale fundamental groups

December 12, 2019 / 16:30 # Abhinandan (IMB)

↕

In topology, the notions of fundamental group and finite covers are very well connected. In fact, for a topological space S, the automorphism group of the fiber functor from the category of finite coverings of S to sets is isomorphic to the profinite completion of the fundamental group of S. In the 1960s, A. Grothendieck adapted this point of view to algebraic geometry by considering finite étale covers of schemes and defined the fundamental group for (connected) schemes. This generalization, when specialized to the case of fields, is the well-known Galois theory for fields. In this talk, after recalling basic definitions and results from topology and Galois theory, we will discuss the étale fundamental group for a (connected, affine) scheme.

Théorèmes spectraux et calculs fonctionnels

December 6, 2019 / 16:30 # COMETX Thomas (IMB)

↕

The best known spectral theorem is that on matrices. He asserts that any real symmetric matrix is diagonalizable in an orthonormal basis. It allows to suppress results like the existence of a positive definite symmetric square root for a positive definite symmetric matrix. More generally, it allows to define f(M) where f is a scalar function and M the matrix in question. This is called a functional calculation. After showing some proofs that can be done with these results, I will talk about the more general spectral theorem on the diagonalization of a self-adjoint operator on a Hilbert space and the functional calculus that follows from it. Finally, I will talk about functional calculus $H^\infty$ where we have to define f(T), where f is a holomorphic function and T an operator on the Banach space. I will explain why it is linked to certain inequalities and I will present some of them that I am studying in my thesis.

Explicit Construction of Abelian Extensions of Number Fields

November 21, 2019 / 16:30 # Jared Asuncion (IMB)

↕

Given a number field K, the twelfth problem of Hilbert asks to construct all abelian extensions of K by adjoining special values of particular analytic functions. In this talk, we will discuss the only two cases in which this problem is completely solved, namely when K is the field of rational numbers and when K is an imaginary quadratic number field.The talk will begin with recalling the necessary definitions from algebraic number theory, including the definition of an abelian extension. We will also define elliptic curves, as an algebraic structure and analytically as a complex torus. After these preliminaries, we will state the main theorems of complex multiplication, which allow us to explicitly solve Hilbert’s twelfth problem foran imaginary quadratic number field K.Towards the end, we will briefly mention the case of CM fields, and how it relates to the case of the imaginary quadratic number field.

Opérateurs pseudo-différentiels

November 13, 2019 / 16:30 # BRUN Pierre (IMB)

↕

In the domain of PDEs pseudo-differential operators appear naturally. In my presentation I will define these operators and present some results and some tools (for example symbolic computation) and I will end up giving a nice proof of the Caldéron-Vaillancourt theorem.

Compter les points d'une courbe sur un corps fini

October 17, 2019 / 16:30 # KIEFFER Jean (IMB)

↕

When C is an algebraic curve defined over a finite field k, the number of k-points of C is finite and we can therefore ask to calculate this reduced number. An important result, de é Schoof for elliptic curves and Pila in the general case, is that there is a counting algorithm in polynomial time. In my presentation, I will present this algorithm and ways to speed it up.