Name: Session régionale du séminaire des doctorant.e.s
Start: 2024-12-12T13:00:00+01:00
End: 2024-12-12T19:00:00+01:00
Location: Institut de mathématiques de Toulouse

Session régionale du séminaire des doctorant.e.s

jeudi 12 décembre 2024 - 13:00

lundi 9 décembre 2024 ¶
mardi 10 décembre 2024 ¶
mercredi 11 décembre 2024 ¶
jeudi 12 décembre 2024 ¶

13:00 Accueil
Accueil
13:00 - 13:30
Room: Amphi Schwartz
13:45 L'apprentissage des polynômes à la transition lycée-université - Juliette Veuillez-Mainard
L'apprentissage des polynômes à la transition lycée-université
- Juliette Veuillez-Mainard
13:45 - 14:15
Room: Amphi Schwartz 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.
14:30 Conformal Object Detection - Léo Andéol
Conformal Object Detection
- Léo Andéol
14:30 - 15:00
Room: Amphi Schwartz 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.
Hölder continuity of solutions to complex Monge-Ampère equations on singular spaces. - Guilherme Cerqueira Gonçalves
Hölder continuity of solutions to complex Monge-Ampère equations on singular spaces.
- Guilherme Cerqueira Gonçalves
14:30 - 15:00
Room: Salle Johnson 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.
15:05 How to prove controllability of a system with fewer controls than components ? - Mathilda Trabut
How to prove controllability of a system with fewer controls than components ?
- Mathilda Trabut
15:05 - 15:35
Room: Amphi Schwartz 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.
Probabilité de retour d'une marche aléatoire sur un groupe libre - Guillaume Chevallier
Probabilité de retour d'une marche aléatoire sur un groupe libre
- Guillaume Chevallier
15:05 - 15:35
Room: Salle Johnson Considérons une mesure de probabilité $μ$ sur un groupe libre $F$ dont le support est fini et engendre le groupe en tant que semi-groupe. Pour $n$ un entier naturel et $x, y \in F$ , notons $p^{(n)} (x, y) := μ^{* n} (x^{- 1} y)$ la probabilité que la marche aléatoire associée à la mesure $μ$ , basée en $x$ atteigne le sommet $y$ en exactement $n$ pas. Alors la séquence de probabilités $(p^{(n)} (x, y))_{n \in N}$ admet un développement asymptotique au sens de Poincaré de la forme: $p^{(n)} (x, y) \sim \frac{C}{n^{3 / 2} R^{n}} (1 + \sum_{k \geq 1} \frac{c_{k}}{n^{k / 2}}),$ où $C > 0$ et $(c_{k})_{k \geq 1}$ sont des constantes dépendantes du couple $(x, y)$ et $R > 1$ est l'inverse du rayon spectral de l'opérateur de Markov associé à la marche aléatoire. Cette estimation est une amélioration d'un résultat dû à Steven P.Lalley, paru en 1993 affirmant que la séquence $(p^{(n)} (x, y))_{n \in N}$ vérifie l’équivalent: $R^{n} n^{3 / 2} p^{(n)} (x, y) \sim C .$
15:40 Dynamics of Polynomial Automorphisms of $C^{2}$ - Adrien Kachkahi
Dynamics of Polynomial Automorphisms of $C^{2}$
- Adrien Kachkahi
15:40 - 16:10
Room: Salle Johnson In this talk, we will explain the dynamics of polynomial automorphisms in $C^{2}$ , 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 $C^{2}$ and give a classification of the Fatou components.
Modeling moderate and extreme urban rainfall at high spatio-temporal resolution - Chloé Serre-Combe
Modeling moderate and extreme urban rainfall at high spatio-temporal resolution
- Chloé Serre-Combe
15:40 - 16:10
Room: Amphi Schwartz 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.
16:30 Session Poster
Session Poster
16:30 - 18:00
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