Belotto Da Silva, Andre Bastien, Fanny Humphries, Donovan

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 t...

Druel, Stéphane Bastien, Fanny Humphries, Donovan

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 s...

Touzet, Frédéric Bastien, Fanny Humphries, Donovan

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.

Druel, Stéphane Bastien, Fanny Humphries, Donovan

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 s...

Araujo, Carolina Bastien, Fanny Humphries, Donovan

In the last few decades, much progress has been made in birational algebraic geometry. The general viewpoint is that complex projective manifolds should be classified according to the behavior of their canonical class. As a result of the minimal model program (MMP), every complex projective manifold can be built up from 3 classes of (possibly singu...

Calum, Spicer Bastien, Fanny Humphries, Donovan

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.

Binyamini, Gal Bastien, Fanny Humphries, Donovan

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 polynomially on the degree of $W$, the logarithmic height o...

Novikov, Dmitry Bastien, Fanny Humphries, Donovan

We consider the structure $\mathbb{R}^{RE}$ obtained from $(\mathbb{R},

Guenancia, Henri Bastien, Fanny Humphries, Donovan

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 s...

Araujo, Carolina Bastien, Fanny Humphries, Donovan

In the last few decades, much progress has been made in birational algebraic geometry. The general viewpoint is that complex projective manifolds should be classified according to the behavior of their canonical class. As a result of the minimal model program (MMP), every complex projective manifold can be built up from 3 classes of (possibly singu...