Prem S. Puri Memorial Lecture

Images From a Strange Land

Dr. Russell Lyons

James H. Rudy Professor in Mathematics at
Indiana University

Start Date and Time: Fri, 19 Apr 2024, 10:30 AM

End Date and Time: Fri, 19 Apr 2024, 11:30 AM

Refreshments: 10:30 a.m. in WTHR 172

Abstract:

Given a discrete set of points in a metric space, called nuclei, one associates to each such nucleus its Voronoi cell, which consists of all points closer to it than to other nuclei. One of the first scientific uses of such a construction was by John Snow in his famous investigation of the mid-19th century cholera epidemic in London. Voronoi diagrams are now widely used in mathematics, science, and engineering; they are used even in baking. In Euclidean space, one commonly uses a homogeneous Poisson point process to assign the locations of the nuclei. As the intensity of the point process tends to 0, the nuclei spread out and disappear in the limit, with each pair of space points eventually belonging to the same cell. Surprisingly, this does not happen in other settings such as hyperbolic space, which is the third-most important geometry after Euclidean and spherical. We will describe properties of such a limiting tessellation, as well as analogous behavior in a discrete setting.