Institut de recherche mathématique avancée

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.