Orderability and groups of dynamical origin (Yash Lodha, University of Hawaii at Manoa)

20.03.2025 16:15 – 17:15

The study of bi-orderable groups has a long history that goes back to seminal work of Dedekind, H older and Hilbert. The study of left orderable groups has more modern origins, and the notion provides a remarkable characterization of whether a countable group admits a faithful action by orientation preserving homeomorphisms on the real line.
In this mini course we will introduce and study these notions.
The first lecture will be an introduction to left orderable and bi-orderable groups,
and shall describe an algebraic point of view.
The second lecture will feature various examples of groups of dynamical origin that naturally emerge as groups of homeomorphisms of the real line and the circle.
The third lecture will describe connections with the analytic notions of second bounded cohomology, rotation numbers, stable commutator length and quasi-morphisms.
The fourth lecture will focus on the space of left orders on a countable group and the Witte-Morris theorem.
Throughout the mini course, I will discuss open problems and new directions of research.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-15, Mini course

entrée libre