07.02.2023

Ana Rechtman (Université de Strasbourg)

Title

Broken books and periodic orbits of Reeb flows in dimension 3

Abstract
Reeb vector fields (or flows) of contact structures form an important family of volume preserving vector fields. On a closed 3-manifold, these vector fields always have at least two periodic orbits. The aim of the talk is to introduce broken book decompositions associated to a Reeb flow and deduce from their existence results on the number of periodic orbits: any non-degenerate Reeb vector field has either two or infinitely many periodic orbits. These are results obtained in collaboration with V. Colin and P. Dehornoy.

As motivation, I will review other results on the existence of periodic orbits for non-singular vector fields and the known examples without periodic orbits. Finally, I will present other applications of broken book decompositions.

Schedule

10:00 - 11:30 RTG Lecture 1 (Ana Chavez Caliz) | 5. OG, Konferenzraum
11:30 - 12:00 Get-Together with speaker | 5. OG, Common Room
12:00 - 13:00 Common lunch | reserved at BräuStadel
13:00 - 13:30 Informal meeting of PhD students | 5. OG, Common Room
13:30 - 14:30 RTG colloquium: Prof. Ana Rechtman | EG Seminarraum B
14:30 - 15:30 Common coffee/tea | 5. OG, Common Room
15:30 - 17:00 RTG Lecture 2 (Wilderich Tuschmann) | 5. OG, Konferenzraum

HD