Mathematics Colloquium: Hyperbolic surfaces and their correlation number

Speaker: Giuseppe Martone, Sam Houston State University

Title: Hyperbolic surfaces and their correlation number 

Abstract:  A surface is a two-dimensional object, like the exteriors of a ball, a donut or a pretzel. Some surfaces can be equipped with a metric coming from the geometry of the hyperbolic plane. Once a surface has this structure, we can make precise geometric measurements on it. For example, if we draw a loop on a hyperbolic surface, we can measure its length. If we look at all possible (carefully drawn) loops on the surface, how many of them have length at most x? If we take two different hyperbolic surfaces, how many (carefully drawn) loops have length roughly equal to x on both surfaces? Do the answers differ if the surface has punctures? In this talk, I will explain the ideas behind these questions, why they are interesting, and what we can say about their answers.

Time:  Friday, October 2, 3:30pm – 4:30pm

Place:  Exploratory Hall, room 4106 or Zoom