Counting arcs of the same type

Geometry & Topology
Event time: 
Tuesday, February 13, 2024 - 4:00pm
KT 205
Marie Trin
Speaker affiliation: 
Université de Rennes
Event description: 

Two closed curves on a hyperbolic surface are said to be of the same type if they differ from a mapping class. The question of counting curves of the same type with bounded length has been studied by M.Mirzakhani who showed that the counting is polynomial into the lenght. Mirzakhani's results were recovered and extended by Erlandsson-Souto proving convergence theorems for certain sequences of measures. In 2022, N.Bell obtained results similar to those of Mirzakhani for arcs of the same type in surfaces with boundary. We will introduce the method based on the convergence of measured for curves counting and then look at a way to adapt it to the case of arcs.