Date: Monday, October 21, 2019
Location: 3866 East Hall (3:00 PM to 4:00 PM)
Title: Counting orbit points and PattersonSullivan 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 PattersonSullivan measure, and we'll see how to construct it, and time permitting, use this to count orbit points of convexcocompact groups.
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Speaker: Sayantan Khan
Institution: UM
Event Organizer:
