Session régionale du séminaire des doctorant.e.s

jeudi 12 déc. 2024, 13:00 → 19:00 Europe/Paris

Institut de mathématiques de Toulouse

Les séminaires des docorant.e.s des instituts de mathématiques de Montpellier et Toulouse, avec le soutien de la fédération occitane de Mathématiques, s'associent pour une session commune. Cette session aura lieu le 12 décembre après-midi à l'institut de mathématiques de Toulouse.

Les inscriptions sont ouvertes via le lien "Inscription." Il est possible de soumettre une présentation orale ou un poster jusqu'au 8 novembre. 

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The doctoral student seminars of the Montpellier and Toulouse mathematics institutes, with the support of the federation OcciMath, are joining forces for a joint session. This session will take place on the afternoon of December 12 at the Institut de Mathématiques in Toulouse.

Registration is open via the “Registration” link. Oral and poster presentations can be submitted until November 8. 

 

Comité d'organisation / Organizing committee

• Candice Bernard (IMT)
• Jan-Luka Fatras (IMT)
• Florian Gossard (IMT)
• Pierrick Le Vourc'h (IMAG)
• Ulysse Mounoud (IMAG)
• Nikola Tomic (IMAG)

avec le soutien de / with  Matthieu Hillairet (OcciMath)

 

 

 

13:00 → 13:30 Accueil

Accueil des participants et présentation des laboratoires de mathématiques en Occitanie.

13:45 → 14:15 L'apprentissage des polynômes à la transition lycée-université¶

Les polynômes et fonction polynomiales sont utilisées et étudiées du collège à l'enseignement supérieur, d'abord à travers les équations polynomiales, fonctions polynomiales, puis en tant qu'objets formels. Dans ma thèse, je m'intéresse spécifiquement à leur apprentissage à la transition lycée-université, période qui a été identifiée comme charnière dans l'enseignement des mathématiques. Dans cet exposé, je présenterai un questionnaire que nous avons fait passé à des élèves de première, de terminale, et des étudiant.es de L1 mathématiques et de classe préparatoire MPSI. Je parlerai en particulier de certains obstacles de la transition lycée-université sur ce sujet, et des difficultés des élèves que ce questionnaire nous a permis d'identifier.

Orateur: Juliette Veuillez-Mainard

14:30 → 15:00 Conformal Object Detection¶

Recent advances in object detectors have led to their adoption for industrial uses. However, their deployment in critical applications is hindered by the inherent lack of reliability of neural networks and the complex structure of object detection models. To address these challenges, we turn to post-hoc procedures like Conformal Prediction, which offer statistical guarantees that are model-agnostic, distribution-free and finite-sample. Our contribution is manifold: first, we formally define the problem of Conformal Object Detection (COD) and introduce a novel method, Sequential Conformal Risk Control (SeqCRC), that extends the statistical guarantees of Conformal Risk Control (CRC) to multiple parameters, as required in the COD setting. Then, we propose some loss functions and prediction sets suited to applying CRC to different applications and certification requirements. Finally, we present a toolkit enabling replication and further exploration of our methods. Using this toolkit, comprehensive experiments have resulted in a benchmark that not only validates the approaches used but is informative on the trade-offs they induce.

Orateur: Léo Andéol

14:30 → 15:00 Hölder continuity of solutions to complex Monge-Ampère equations on singular spaces.¶

In recent years, the use of PDEs and pluripotential theory have produced important results in both differential and algebraic complex geometry. In this talk, I will study, using pluripotential theory, the modulus of continuity of solutions to Dirichlet problems for complex Monge-Ampère equations with Lp densities on a domain inside a complex analytic space with isolated singularities. Moreover, obtaining that if the boundary data is Hölder, then so is the solution outside of the singular set.

Orateur: Guilherme Cerqueira Gonçalves

15:05 → 15:35 How to prove controllability of a system with fewer controls than components ?¶

Given an ODE or a PDE, we may ask whether we can achieve a prescribed behavior for the solution by acting on the system through a control (e.g., a source term). This is the goal of controllability theory in a nutshell. Controllability can be challenging when there are fewer controls than components in the system.
We will start by examining the case of ODEs (Kalman rank condition), then consider parabolic equations in 1D (moment method), and finally, if time permits, discuss the multi-dimensional case in specific geometries.

Orateur: Mathilda Trabut

15:05 → 15:35 Probabilité de retour d'une marche aléatoire sur un groupe libre¶

Considérons une mesure de probabilité $\mu$ sur un groupe libre $\mathbb{F}$ dont le support est fini et engendre le groupe en tant que semi-groupe. Pour $n$ un entier naturel et $x,y\in \mathbb{F}$, notons $p^{(n)}(x,y):={\mu }^{\ast n}(x^{-1}y)$ la probabilité que la marche aléatoire associée à  la mesure $\mu$, basée en $x$ atteigne le sommet $y$ en exactement $n$ pas. Alors la séquence de probabilités
$(p^{(n)}(x,y){)}_{n\in \mathbb{N}}$ admet un développement asymptotique au sens de Poincaré de la forme:
$$p^{(n)}(x,y)\sim \frac{C}{n^{3/2}{R}^n}(1+\sum _{k\ge 1}\frac{c_k}{n^{k/2}}),$$ où $C>0$ et $(c_k){k\geq 1}$sontdesconstantesdépendantesducouple$(x,y)$et$R>1$est{l}^{\prime }inversedurayonspectralde{l}^{\prime }opérateurdeMarkovassociéàlamarchealéatoire.Cetteestimationestuneamélioration{d}^{\prime }unrésultatdûàStevenP.Lalley,paruen1993affirmantquelaséquence$(p^{(n)}(x,y)){n\in\mathbb{N}}$vérifie{l}^{\prime }équivalent:$$R^n{n}^{3/2}{p}^{(n)}(x,y)\sim C.$$

Orateur: Guillaume Chevallier

15:40 → 16:10 Dynamics of Polynomial Automorphisms of C2¶

In this talk, we will explain the dynamics of polynomial automorphisms in ${\mathbf{C}}^2$, focusing on the dynamics of Hénon mappings.
We will recall some basic facts about the dynamics of polynomials in one variable. We will pay particular attention to the partition of the plane into the Julia and Fatou sets.
Then, we will study the analogous partition of ${\mathbf{C}}^2$ and give a classification of the Fatou components.

Orateur: Adrien Kachkahi

15:40 → 16:10 Modeling moderate and extreme urban rainfall at high spatio-temporal resolution¶

Precipitation modeling is of great interest for flood risk analysis. We propose to model the distribution of urban precipitation measured at high spatial and temporal resolution by the Montpellier Urban Observatory rain gauge network over four years of measurements. We combine them with radar reanalysis data to extend our analysis to a longer period with less fine resolution. For our modeling approach, we simultaneously consider moderate and intense rainfall by using the Extended Generalised Pareto Distribution (EGPD)
to avoid explicit threshold selection, often tricky in extreme statistics, and to reduce the
complexity of parameter estimation. We also model the spatio-temporal dependence by incorporating advection through a spatio-temporal Brown-Resnick process. We use indices of extreme autocorrelation, to show its variability between locations in relation to their spatial distances and to the temporality of the measurements. We will highlight the importance of including advection by comparing it with a simpler separable model.

Orateur: Chloé Serre-Combe

16:30 → 18:00 Session Poster¶

Jérémy Boyer (IMT) "Gaussian approximation of non stationary empirical processes."
Grégoire Cha (IMAG) TBA
Junyi Chen (IMAG) "Multi-step Model Reduction for Coagulation Schemes"
Daniela Corbetta (Padova) "Conformal inference for cell type annotation with graph-structured constraints"
Florian Gossard (IMT) TBA
Pierrick Le Vourc'h (IMAG) "Dérivation d’un modèle moyenné pour un écoulement diphasique compressible stratifié"
Hugo Marsan (IMT) "Zero-noise limit measures of perturbed cellular automata"
Paul Pace (IMT) "Sparse-SPIC methods of 4th order tailored to the Vlasov-Poisson Equation"
Angel Reyero (IMT) TBA