# Canal-U

Mon compte

## Institut Fourier

L’Institut Fourier, laboratoire de mathématiques de Grenoble, est une unité mixte de recherche CNRS/Université Grenoble Alpes. Ses activités portent principalement sur les mathématiques fondamentales développées autour de six grands thèmes de recherche : algèbre et géométries, combinatoire et didactique, géométrie et topologie, physique mathématique, probabilités, théorie des nombres. Ses recherches s’ouvrent aussi à d’autres disciplines, telles que la biologie, l’informatique et la physique. Depuis 2011, l’Institut Fourier filme ses évènements scientifiques tels que : colloques, séminaires, écoles d’été, conférences grand public, …

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### Liste des programmes

We will discuss some recent work on the minimal model program (MMP) for foliations and explain some applications of the MMP to the study of foliation singularities and to the study of some hyperbolicity properties of foliated pairs. This features joint work with P. Cascini and R. Svaldi.
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.
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 ...
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 ...
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 ...
Let X be a holomorphic symplectic manifold and D a smooth hypersurface in X. Then the restriction of the symplectic form on D has one-dimensional kernel at each point. This distribution is called the characteristic foliation. I shall survey a few results concerning the possible Zariski closure of a general ...
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 ...
We consider an algebraic $V$ variety and its foliation, both defined over a number field. Given a (compact piece of a) leaf $L$ of the foliation, and a subvariety $W$ of complementary codimension, we give an upper bound for the number of intersections between $L$ and $W$. The bound depends ...
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 ...
I will discuss dynamical properties of the Jouanolou foliation of the complex projective plane in degree two. Joint work with Aurélien Alvarez.