Le séminaire des doctorants se propose de fournir aux doctorants une occasion de s'ouvrir aux autres domaines des mathématiques que le leur. A chaque séance, un intervenant réalise un exposé sur un fait standard de leur domaine d'étude, de niveau adapté à l'ensemble des doctorants.

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In this talk I will present the basic context of measured dynamics, and more specifically of ergodic theory on standard measured spaces. After redefining standard measure spaces, measure-preserving bijections and ergodicity, The focus of my talk will be to expose some examples. The odometer, is a very classical example of an ergodic bijection preserving a probability measure, but obtaining examples of infinite measure-preserving ergodic bijections (IMPEB) is a "non-trivial task". I will use two different representations of the odometer to present two general classes of IMPEB, the Kakutani skyscrapers and the infinite Rank-one bijections. While the definitions will be a bit informal to avoid drowning in technical details, I will integrate as many drawings as I can to give the intuition behind the constructions. If time allows, I will give some properties that these classes of IMPEB satisfy, in order to explain why they are so central in the theory, and/or give some sketches of proofs.

The PhD students seminar aims to provide PhD students with an opportunity to explore other areas of mathematics beyond their own. At each session, a speaker gives a presentation on a standard topic in their field of study, at a level suitable for all doctoral students.