Séminaires : Phd Seminar - Séminaire des doctorant.e.s

Le séminaire des doctorant.e.s est l'occasion pour les doctorant.e.s de présenter des résultats et des problématiques dignes d'intérêt devant un public de non-spécialistes. L'ambiance y est informelle ; poser des questions naïves est encouragé, et les questions moins naïves sont bienvenues dans la mesure où elles n'entravent pas le bon déroulement de l'exposé.

Chaque jeudi à 18h, en alternance entre Jussieu et Sophie Germain.

The PhD seminar is an opportnuity for PhD students to present results and topics worthy of interest in front of a non-specialist audience. The mood is informal ; asking naive questions is highly encouraged and less naive questions are also welcomed, as long as they don't intefere with the smoothness of the talk.

Every Thursday at 6pm, alternating between Jussieu and Sophie Germain.

Let $F : (\mathbb{C}^n, 0) \to (\mathbb{C}^n, 0)$ be a tangent to the identity germ of biholomorphism, that is, $D_0 F = Id$. If n=1, the local dynamics of such a map are entirely described by Leau and Fatou's flower theorem. In higher dimensions, there is no result that describes the dynamics of generic tangent to the identity maps. In this talk, we will first present a result of Abate that reduces the study of tangent to the identity maps in dimension 2 to only three "reduced" forms. We will then show how Abate's theorem can be exploited to study the dynamics of these maps in dimension 2. Finally, we will see how some of these results translate in higher dimensions.