le (58m26s)

# Résultats de recherche

**3535**

le (54m38s)

## S. Druel - A decomposition theorem for singular spaces with trivial canonical class (Part 5)

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 (58m10s)

## A. Höring - A decomposition theorem for singular spaces with trivial canonical class (Part 3)

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 (1h36s)

## H. Guenancia - A decomposition theorem for singular spaces with trivial canonical class (Part 2)

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 (59m19s)

## J. Aramayona - MCG and infinite MCG (Part 1)

The first part of the course will be devoted to some of the classical results about mapping class groups of finite-type surfaces. Topics may include: generation by twists, Nielsen-Thurston classification, abelianization, isomorphic rigidity, geometry of combinatorial models. In the second part we will explore some aspects of "big" mapping class groups, highlighting the analogies and differences with their finite-type counterparts, notably around isomorphic rigidity, abelianization, and geometry of combinatorial models. Voir la vidéole (1h1m4s)

## B. Deroin - Monodromy of algebraic families of curves (Part 1)

The mini-course will focus on the properties of the monodromies of algebraic families of curves defined over the complex numbers. One of the goal will be to prove the irreducibility of those representations for locally varying families (Shiga). If time permit we will see how to apply this to prove the geometric Shafarevich and Mordell conjecture. The material that will be developed along the lectures are - analytic structure of Teichmüller spaces - theory of Kleinian groups - Bers embedding - b-groups - Mumford compactness criterion - Imayoshi-Shiga finiteness theorem. Voir la vidéole (1h11m15s)

## B. Deroin - Monodromy of algebraic families of curves (Part 3)

The mini-course will focus on the properties of the monodromies of algebraic families of curves defined over the complex numbers. One of the goal will be to prove the irreducibility of those representations for locally varying families (Shiga). If time permit we will see how to apply this to prove the geometric Shafarevich and Mordell conjecture. The material that will be developed along the lectures are - analytic structure of Teichmüller spaces - theory of Kleinian groups - Bers embedding - b-groups - Mumford compactness criterion - Imayoshi-Shiga finiteness theorem. Voir la vidéole (1h1m41s)

## S. Filip - K3 surfaces and Dynamics (Part 2)

K3 surfaces provide a meeting ground for geometry (algebraic, differential), arithmetic, and dynamics. I hope to discuss:- Basic definitions and examples- Geometry (algebraic, differential, etc.) of complex surfaces- Torelli theorems for K3 surfaces- Dynamics on K3s (Cantat, McMullen)- Analogies with flat surfaces- (time permitting) Integral-affine structures Voir la vidéole (1h1m18s)

## S. Filip - K3 surfaces and Dynamics (Part 3)

K3 surfaces provide a meeting ground for geometry (algebraic, differential), arithmetic, and dynamics. I hope to discuss:- Basic definitions and examples- Geometry (algebraic, differential, etc.) of complex surfaces- Torelli theorems for K3 surfaces- Dynamics on K3s (Cantat, McMullen)- Analogies with flat surfaces- (time permitting) Integral-affine structures Voir la vidéole (1h4m55s)