MASCOS - ANALYSIS SEMINAR
Published on the 08 Mar 2005
ANALYSIS SEMINAR
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.