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 Accueil

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

1 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-Menard

2 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

3 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

4 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

5 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:
$$ p^{(n)}(x,y)\sim \frac{C}{n^{3/2} R^n} \left(1+\sum_{k\geq 1} \frac{c_k}{n^{k/2}}\right), $$ 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 $(p^{(n)}(x,y)){n\in\mathbb{N}}$ vérifie l’équivalent: $$R^n n^{3/2} p^{(n)}(x,y)\sim C.$$

Orateur: Guillaume Chevallier

6 Computational methods for hidden semi-Markov models with mixed effects - applications to plant branching models

In the framework of plant development modelling, statistical models can be divided into two categories. The first one, referred to as 'genotype x environment', is based on mixed models, which do not account for time dependencies existing in the considered processes. The second category is based on sequence analysis models that are funded on biological models, but currently do not account for genotype or environmental effects.
More specifically, we are here focused on hidden semi-Markov models, introduced about 20 years ago (Guédon et al., 2001) to model dynamical aspects of plant structure development. These models allow modellers to account for different development phases of either plants or their components (branches, roots, etc) through hidden states. The PhD proposal aims at including fixed and random effects within this category of models, the former aiming at characterising the effects of targeted covariates (genotype and environment) ant the latter, to account for constraints related to experimental design. The work to be accomplished, beyond model specification, is to develop inference algorithms suited to the specific complexity of these models .
Beyond plant developement modelling, the methodological advances obtained in the hidden semi-Markov framework will enrich this family of models and offer new possibilities for addressing scientific questions in various domains of application (health, seismology, reliability, ecology, etc).

Orateur: Mathieu Valdeyron

7 TBA

TBA

Orateur: Adrien Kachkahi

8 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