401-3218-19L  Groups Acting on the Circle

SemesterFrühjahrssemester 2019
DozierendeN. Matte Bon
Periodizitäteinmalige Veranstaltung
LehrspracheEnglisch


KurzbeschreibungThe circle is one of the simplest space appearing in mathematics. Group actions on the circle enjoy a rich theory, going from the work of Poincaré at the turn of the XXth century to a currently active field of research. This theory is a common meeting ground of several fields including group theory, dynamics, hyperbolic geometry and rigidity theory. (Lecturer: N. Matte Bon)
LernzielFamiliarise with the theory of group actions on the circle and on the real line by homeomorphisms and diffeomorphisms. This will also be a pretext to get acquainted with some fundamental notions in modern group theory and in dynamics.
InhaltThe course will begin with the classical theory of rotation number of Poincaré and Denjoy, and then move to the study of groups of homeomorphisms of the circle and of the real line. Along the way, there will be a short introduction to amenability of groups, which plays a role in this setting.
Time permitting and depending on the interests of the class, we might have a glance to Kazhdan's property (T), to actions of lattices on the circle, or give a short introduction to bounded cohomology.
Voraussetzungen / BesonderesBasic group theory and real analysis.