10 December – Stavroula Makri (VU Amsterdam)
Title: Braids and fixed points
Abstract: The use of braid group theory in surface dynamics and Nielsen fixed point theory was initiated in the early 1980s and has since played a key role in studying fixed points and periodic orbits of surface homeomorphisms. In this talk, I will begin with a basic introduction to Nielsen fixed point theory and braid group theory, and then explain how a braid can be associated with a homeomorphism of a compact surface isotopic to the identity that leaves a finite set invariant. We will see how braid theory can be applied to obtain important results and information about surface homeomorphisms. In particular, I will discuss an elegant result showing that the matrix representation of a braid provides valuable information about the existence and linking behavior of its fixed points, and how we can extend it to a 3-dimensional setting.