Equivalent curves in surfaces- Anja Bankovic

Conference Title: GEAR Retreat 2012 Theme: Junior Talks (12 of 12) Title: Equivalent curves in surfaces Speaker: Anja Bankovic, Univ. of Illinois at Urbana-Champaign; Date and Time: Friday August 3, 16:30 Description: In this talk we'll discuss length functions on a variety of spaces of metrics on a genus g > 1 surface. In particular, we will examine a phenomenon first observed by Horowitz and Randol that there are arbitrary large sets of homotopy classes of closed curves on a surface whose lengths are equal in every hyperbolic metrics. We will consider the family of nonpositively curved singular flat metrics and show that this phenomenon persists in a large subfamily of flat metrics coming from q-differentials. However in the limit the phenomenon disappears. Sponsor: GEAR Network Local host: UIUC Department of Mathematics Funding provided by: National Science Foundation Research Networks in Mathematical Sciences programAbstract: Anja Bankovic, in this GEAR Retreat 2012 Junior Talk, will discuss length functions on a variety of spaces of metrics on a genus g > 1 surface, especially homotopy classes of closed curves on some surfaces.