Date: Monday, October 21, 2019
Location: 3866 East Hall (3:00 PM to 4:00 PM)
Title: Counting orbit points and Patterson-Sullivan measures
Abstract: In this talk, we'll see how one counts the orbit points under the action of a cocompact lattice (i.e. the fundamental group of a compact hyperbolic surface), and how tools from dynamics are useful in doing so. We will then attempt to do the same for a larger class of groups, namely convex cocompact groups (which are fundamental groups of certain infinite volume hyperbolic surfaces), and in the attempt, discover the need for a measure on the boundary of the hyperbolic space with certain remarkable properties. This will be the Patterson-Sullivan measure, and we'll see how to construct it, and time permitting, use this to count orbit points of convex-cocompact groups.
Files:
Speaker: Sayantan Khan
Institution: UM
Event Organizer:
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