Department of

January 2019February 2019March 2019 Su Mo Tu We Th Fr Sa Su MoTuWe Th Fr Sa Su Mo Tu We Th Fr Sa 1 2 3 4 5 1 2 1 2 6 7 8 9 10 11 12 3 4 5 6 7 8 9 3 4 5 6 7 8 9 13 14 15 16 17 18 19 10 11 12 13 14 15 16 10 11 12 13 14 15 16 20 21 22 23 24 25 26 17 181920 21 22 23 17 18 19 20 21 22 23 27 28 29 30 31 24 25 26 27 28 24 25 26 27 28 29 30 31

Thursday, February 14, 2019

**Abstract:** When geometric structures on surfaces are determined by the lengths of curves, it is natural to ask which curves’ lengths do we really need to know? It is a classical result of Fricke that a hyperbolic metric on a surface is determined by its marked simple length spectrum. More recently, Duchin–Leininger–Rafi proved that a flat metric induced by a unit-norm quadratic differential is also determined by its marked simple length spectrum. In this talk, I will describe a generalization of the notion of simple curves to that of q-simple curves, for any positive integer q, and show that the lengths of q-simple curves suffice to determine a non-positively curved Euclidean cone metric induced by a q-differential metric.