The problem of uniformly distributing a large number of points
on smooth manifolds of fixed dimension d+1 with d>0 such as the
d-sphere, is an interesting and difficult problem with numerous
applications. On the circle, the nth roots of unity are an obvious
choice.
In this talk we will begin by showing how to construct "good" points on
d-spheres using finite fields. We will then show how this problem
relates to various important concepts in classical and applied
analysis such as Riesz energy, t-designs and
numerical integration. If time permits, we will briefly discuss some
further applications to mathematical biology and combinatorics such as
scar defects in biological systems and the
construction of positive codes.
This talk will be accessible to undergraduate and graduate students.
|