le (55m58s)

# Résultats de recherche

**888**

le (57m38s)

## S. Druel - A decomposition theorem for singular spaces with trivial canonical class (Part 4)

The Beauville-Bogomolov decomposition theorem asserts that any compact Kähler manifold with numerically trivial canonical bundle admits an étale cover that decomposes into a product of a torus, an irreducible, simply-connected Calabi-Yau, and holomorphic symplectic manifolds. With the development of the minimal model program, it became clear that singularities arise as an inevitable part of higher dimensional life. We will present recent works in which a singular version of the decomposition theorem is established. Voir la vidéole (1h6m50s)

## A. Belotto da Silva - Singular foliations in sub-Riemannian geometry and the Strong Sard Conjecture

Given a totally nonholonomic distribution of rank two $\Delta$ on a three-dimensional manifold $M$, it is natural to investigate the size of the set of points $\mathcal{X}^x$ that can be reached by singular horizontal paths starting from a same point $x \in M$. In this setting, the Sard conjecture states that $\mathcal{X}^x$ should be a subset of the so-called Martinet surface of 2-dimensional Hausdorff measure zero. I will present a reformulation of the conjecture in terms of the behavior of a (real) singular ... Voir la vidéole (1h5m16s)

## J. Demailly - Existence of logarithmic and orbifold jet differentials

Given a projective algebraic orbifold, one can define associated logarithmic and orbifold jet bundles. These bundles describe the algebraic differential operators that act on germs of curves satisfying ad hoc ramification conditions. Holomorphic Morse inequalities can be used to derive precise cohomology estimates and, in particular, lower bounds for the dimensions of spaces of global jet differentials. A striking consequence is that, under suitable geometric hypotheses, the corresponding entire curves must satisfy nontrivial algebraic differential equations. These results extend those obtained by ... Voir la vidéole (59m9s)

## S. Ghazouani - Isoholonomic foliations of moduli spaces of Riemann surfaces

In this talk, I will introduce families of foliations on the moduli space of Riemann surfaces M_{g,n} which we call Veech foliations. These foliations are defined by identifying M_{g,n} to certain moduli spaces of flat structures and were first defined by Bill Veech. I will try to expose their specificities, both of geometric and dynamical nature. If time permits I will try to illustrate how the case g=1 is linked to certain differential equations whose solutions are special functions of distinguished interest. This is joint work with ... Voir la vidéole (1h1m35s)

## L. Meersseman - Kuranishi and Teichmüller

Let X be a compact complex manifold. The Kuranishi space of X is an analytic space which encodes every small deformation of X. The Teichmüller space is a topological space formed by the classes of compact complex manifolds diffeomorphic to X up to biholomorphisms smoothly isotopic to the identity. F. Catanese asked when these two spaces are locally homeomorphic. Unfortunatly, this almost never occurs. I will reformulate this question replacing these two spaces with stacks. I will then show that, if X is Kähler, ... Voir la vidéole (1h3m21s)

## F. Touzet - About the analytic classification of two dimensional neighborhoods of elliptic curves

I will investigate the analytic classification of two dimensional neighborhoods of an elliptic curve C with trivial normal bundle and discuss the existence of foliations having C as a leaf. Joint work with Frank Loray and Sergey Voronin. Voir la vidéole (1h2m21s)

## F. Andreatta - The height of CM points on orthogonal Shimura varieties and Colmez conjecture (part1)

We will first introduce Shimura varieties of orthogonal type, their Heegner divisors and some special points, called CM (Complex Multiplication) points. Secondly we will review conjectures of Bruinier-Yang and Buinier-Kudla-Yang which provide explicit formulas for the arithmetic intersection of such divisors and the CM points. We will show that they imply an averaged version of a conjecture of Colmez. Finally we will present the main ingredients in the proof of the conjectures. The lectures are base on joint works with E. Goren, ... Voir la vidéole (1h30m57s)

## F. Andreatta - The height of CM points on orthogonal Shimura varieties and Colmez conjecture (part2)

We will first introduce Shimura varieties of orthogonal type, their Heegner divisors and some special points, called CM (Complex Multiplication) points. Secondly we will review conjectures of Bruinier-Yang and Buinier-Kudla-Yang which provide explicit formulas for the arithmetic intersection of such divisors and the CM points. We will show that they imply an averaged version of a conjecture of Colmez. Finally we will present the main ingredients in the proof of the conjectures. The lectures are base on joint works with E. Goren, ... Voir la vidéole (1h1m34s)