Moduli spaces of stable maps in genus bigger than zero include many components of different dimensions meeting each other in complicated ways, and the closure of the smooth locus is difficult to describe. We will look at examples of genus one and two maps of low degree in the projective plane to get a feeling of how complicated these spaces can be.

Afterwords, we will sketch the construction of a modular desingularization of the space of genus 2 maps to projective spaces using combinatorial techniques from tropical geometry and maps from certain exotic curve singularities.

Given a closed 4-manifold X with an indefinite intersection form, we consider smoothly embedded surfaces in X-int(B^4), with boundary a given knot K in the 3-sphere. We give several methods to bound the genus of such surfaces in a fixed homology class. Our techniques include adjunction inequalities from Heegaard Floer homology and the Bauer-Furuta invariants, and the 10/8 theorem. In particular, we present obstructions to a knot being H-slice (that is, bounding a null-homologous disc) in a 4-manifold and show that the set of H-slice knots can detect exotic smooth structures on closed 4-manifolds. This is joint work with Ciprian Manolescu and Lisa Piccirillo.

Considering a Poisson process observed on a bounded, fixed interval, we are interested in the problem of detecting an abrupt change in its distribution, characterized by a jump in its intensity. Formulated as an off-line change-point problem, we address two distinct questions : the one of detecting a change-point and the one of estimating the jump location of such change-point once detected. This study aims at proposing a non-asymptotic minimax testing set-up, first to construct a minimax and adaptive detection procedure and then to give a minimax study of a multiple testing procedure designed for change-point localisation.

Mathieu Ribatet vous invite à une réunion Zoom planifiée.

Sujet : Séminaire de Fabrice Grela Heure : 9 févr. 2021 11:00 AM Paris

Participer à la réunion Zoom https://ec-nantes.zoom.us/j/99612428063

In this talk, I will introduce you to two important classes of symplectic manifolds: toric manifolds, which are equipped with an effective Hamiltonian action of the torus, and Weinstein manifolds, which come with a handle decomposition compatible with its symplectic structure. I will then show you an algorithm which produces the Weinstein handlebody diagram for the complement of a smoothed toric divisor in a "centered" toric 4-manifold. This is based on joint work with Acu, Capovilla-Searle, Gadbled, Marinković, Murphy, and Starkston.

Joint models for longitudinal and survival data are now widely used in biostatistics to address a variety of etiological and predictive questions. Originally designed to simultaneously analyze the trajectory of a single marker measured repeatedly over time, and the risk of a single right-censored time-to-event, joint models now need to capture increasingly complex longitudinal information to adapt to in-depth medical research questions. After an introduction of the general joint modelling methodology, I discuss two extensions proposed to handle multivariate repeated marker information: one using a latent class approach and one using a latent degradation process approach. The models are illustrated on real data, in particular to describe the progression of Multi-System Atrophy, a rare neurodegenerative disease.

Un problème de contrôle optimal est associé à un système dynamique de la forme y'=f(y,a), où le paramètre a est un contrôle fixé par l'opérateur et à un coût que l'on cherche à minimiser. L'approche de Bellman consiste à étudier la fonction valeur du problème. Celle-ci est solution de viscosité d'une équation de Hamilton-Jacobi-Bellman. Depuis 2013, une théorie des équations de H-J posées sur un réseau a été développée (Achdou-Camilli-Cutri-Tchou et Imbert-Monneau-Zidani), associées justement à un système dynamique évoluant sur cette structure. Dans cet exposé je parlerai de la théorie des solutions de viscosité et des équations de Hamilton Jacobi, et je présenterai le travail que j'effectue en thèse, qui consiste à essayer d'approcher un problème de contrôle sur le réseau à partir d'une suite de problèmes de contrôles posés sur tout l'espace. Plus précisément, on démarre d'un système dynamique contrôlé dans tout le plan auquel on ajoute un terme de pénalisation pour ramener les solutions vers un réseau du plan et on cherche le problème limite qui devrait être un problème de contrôle posé sur le réseau.