30 April - 2 May
Title: Braid groups and non-positive curvature
Abstract: The classical theory of non-positive curvature (as found for example in Bridson and Haefliger) is well established, highly studied and an important part of geometric group theory. In this short course I briefly review the main theorems that can be used to construct non-positively curved spaces and groups. Then I highlight the limitations of these constructions by focusing on a concrete collection of piecewise Euclidean classifying spaces for the braid groups which are highly likelyto be non-positively curved, but which are not yet known to be non-positively curved even after multiple investigations. I conclude by describing some partial progress that my coauthors (Michael Dougherty and Stefan Witzel) and I have made on this question.