School of Mathematics and Statistics - News - MASCOS

Speaker: Mr Johann S Brauchart
University of Technology Graz, Austria

Title: Points on the sphere and some Proof Techniques

Date: Wednesday March 9th
Time: 2:00 pm
Place: Room 3084, Rec Centre

Abstract:

In dealing with points on an unit sphere in an Euclidean
space $\mathbb{R}^{d+1}$, $d\geq2$, which are 'good' in some sense,
one faces certain technical difficulties to answer questions like

What are the explicit coordinates of such points?
How good do such points approximate the uniform measure on the sphere ---> 'equidistribution' ?
How can this be quantified ---> 'discrepancy(-bounds)' ?
What is the distance of two closest points--> well-separation' ?
What is their 'Riesz-$s$-energy' when these points are thought to interact through a Riesz-potential $1/r^s$.
If these points are used as nodes for a numerical integration rule what can be said about the error of integration ---> 'worst-case error bounds' ?

We want to consider some of these questions and look mostly at the techniques used to prove results.