Mathematics Colloquium 2014 - 2015
All seminars are held in Room E/0.15, Senghennydd Road, Cardiff at 15:10 unless stated otherwise.
8th October 2014
Speaker: Prof. 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.
5th November 2014
Speaker: Prof. Alison Etheridge (University of Oxford)
Title: Modelling evolution in a spatial continuum.
Abstract: The basic challenge of mathematical population genetics is to understand the relative importance of the different forces of evolution in shaping the genetic diversity that we see in the world around us. This is a problem that has been around for a century, and a great deal is known. However, a proper understanding of the role of a population's spatial structure is missing. Recently we introduced a new framework for modelling populations that evolve in a spatial continuum. In this talk we briefly describe this framework before outlining some preliminary results on the importance of spatial structure for natural selection..