Title: Non-unique Ergodicity on the Boundary of Outer Space

Speaker: Sanghoon Kwak (KIAS)

Abtract: The Culler--Vogtmann's Outer space CV_n is a space of marked metric graphs, and it compactifies to a set of F_n-trees. Each F_n-tree on the boundary of Outer space is equipped with a length measure, and varying length measures on a topological F_n-tree gives a simplex in the boundary. The extremal points of the simplex correspond to ergodic length measures. By the results of Gabai and Lenzhen-Masur, the maximal simplex of transverse measures on a fixed filling geodesic lamination on a complete hyperbolic surface of genus g has dimension 3g-4. In this talk, we give the maximal simplex of length measures on an arational Fn-tree has dimension in the interval [2n-7, 2n-2]. This is a joint work with Mladen Bestvina, and Elizabeth Field.

* 참가 Zoom 회의 
https://us06web.zoom.us/j/83540915663?pwd=Eu4WYFDWUxun53COoBaQmYNjwa5LaS.1 

* 회의 ID: 835 4091 5663 
* 암호: set2024