Mathematics Colloquium 8 October 2014 – Speaker: Professor Florin Boca

• Date: 8 October 2014
• Speaker: Professor Florin Boca (University of Illinois at Urbana-Champaign)
• Title: Irregularities in the distribution of Euclidean and hyperbolic lattice angles.

Abstract

Spacing statistics measure the randomness of uniformly distributed sequences, or more generally increasing sequences of finite sets of real numbers. A familiar example of a uniformly distributed sequence of sets isgiven by the directions of vectors joining a fixed point in the Euclidean plane, with all (or only visible) points of integer coordinates inside balls of fixed center and increasing radius. However, these directions are not randomly distributed, and even the study of their most popular spacing statistics, limiting gap distribution and pair correlation function, turn out to pose challenges.

This talk will discuss recent progress in the study of the spacing statistics for this type of geometric configuration, comparing the Euclidean and the hyperbolic situations.