À venir

Résumé : In this talk we will consider lightlike geodesics in Lorentzian manifolds. We will focus on the model space of conformal Lorentzian geometry, namely the Einstein’s universe. It is known that the space of these geodesics is a contact manifold. In the four-dimensional case, we will present a way to see that it is actually equipped with a Lorentzian CR structure. In this framework, we will partially describe the contact structure thanks to this additional geometric data.

Résumé : TBA

Résumé : In our talk, we will present an extension of arithmetic intersection theory of adelic divisors on quasi-projective varieties introduced by Yuan–Zhang to the case where these divisors are not necessarily arithmetically nef. The key tool to realize this extension is the concept of relative finite energy established by T. Darvas et al.. In particular, our theory will allow to compute heights on mixed Shimura varieties, e. g., the arithmetic self-intersection number of the line bundle of Siegel–Jacobi forms on the universal abelian variety. This is joint work with José Burgos Gil.

Résumé : The aim of this talk is to explore several historical optimization problems together, namely Dido’s problem and the brachistochrone problem, by adopting an optimal control perspective. We start by introducing optimal control theory. This mathematical discipline consists in determining the best way to influence a dynamical system through a control or input so as to steer it toward a target state [control], while minimizing or maximizing a given cost functional [optimal]. Optimal control theory is used in a wide range of fields, including aerospace engineering (rocket trajectory optimization), finance (optimal portfolio management), and biology (population management). We focus on the case where a dynamical system is described by ordinary differential equations and we present Pontryagin’s Maximum Principle. An outline of the proof, aimed at providing insight into this principle, will also be given. Finally, we apply this framework to the historical problems mentioned above.

Résumé : Résumé : I will give a leisurely, elementary introduction to these two subjects, and then describe some recent progress on the so-called enumerative P=W conjecture, which provides a surprising link between the moduli spaces of Higgs bundles and integrable systems.

Résumé : Dans la classification des surfaces algébriques, les surfaces d'Enriques sont des quotients de surfaces K3 par une involution sans points fixes. En dimension supérieure, cette notion se généralise et l'on introduit les variétés d'Enriques et, dans le cas singulier, les variétés log-Enriques. Dans cet exposé, je présenterai et discuterai plusieurs exemples, j'introduirai les définitions et j'expliquerai les propriétés générales des variétés d'Enriques et des variétés log-Enriques. En particulier je parlerai des variétés log-Enriques qui sont obtenues comme quotients de variétés de Fermat généralisées. Ces dernières ont été étudiées récemment par Hidalgo, Hughes et Leyton-Alvarez. Les résultats que je présenterai viennent de plusieurs articles en collaboration avec S. Boissière, C. Camere, M. Nieper-Wisskirchen et d'un travail en cours avec A. Palomino.

Résumé : TBA