Viveka Erlandsson

University of Bristol


Long random multi-curves


Geometry and Topology Seminar


24th September 2024, 2:00 pm – 3:00 pm
Fry Building, 2.04


It is a classical result due to Huber that the growth of the number of closed geodesics on a closed hyperbolic surface is asymptotic to eLL. In her thesis, Mirzakhani studied the subset of simple (multi) geodesics and proved the asymptotic then is instead polynomial, and later generalized this to counting inside a mapping class group orbit of a fixed (simple or not) closed multi geodesic. Once one can count one can ask what a random multi geodesic of fixed type looks like. For example, how do the length of the individual components distribute? Mirzakhani answered this for random pants decompositions of a hyperbolic surface and this result has been generalized independently by Mingkun Liu and Francisco Arana-Herrera to other simple multi-curves. In this talk I will give a brief overview of these results and then explain how it can be extended to general multicurves and a large class of metrics besides hyperbolic. This is joint work with Juan Souto.






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