## 2 événements

• Séminaire de lecture M2 Maths Pures

### Lundi 4 décembre 10:00-12:00 - Quentin Karegar

The Fundamental group and covering spaces

Résumé : First, we introduce a global topological invariant $\pi_1(X)$ which generalize, in some sense, the number of connected components of a topological (locally path-connected) space $X$. It turns out that the $\pi_1(X)$ is a group and its computation relies on the automorphisms of an appropriate covering space verifying $\pi_1(\tildeX)=0$ (the universal cover). To illustrate these notions, we compute it for some classical examples such as spheres, projective spaces, …
If it remains some time, we will see how $\pi_1$ and covering arise in Riemannian geometry (flat vector bundle, exponential map)

• Séminaire doctorants Picard

### Lundi 4 décembre 13:30-14:30 - Van Tu Le

Dynamique des Endomorphismes Post-critiquement Algébriques

Résumé : We are interested in the study of the dynamics of a holomorphic endomorphism F of \mathbbCP^n, that is the asymptotic behaviour of iterates of F. Fixed points and critical points play a crucial role in such a study. In dimension 1, William Thurston provides a classification allowing us to understand the dynamics of "post-critically finite maps", that is rational functions on the Riemann sphere such that every critical point is (pre-)periodic. The analogue case of higher dimension is that of the so-called post-critically algebraic holomorphic endormorphisms of \mathbbCP^n. In this talk, I will present part of my work in the generalisation to higher dimension of the following property of post-critically finite rational maps : the multiplier of a post-critically finite rational map f at one of its periodic points is either 0 or strictly bigger than 1.

Lieu : Salle Picard (1R2)