A random walk through numerical integration, Riesz configurations and low discrepancy sequences on rectifiable sets

Many practical problems in elasticity, vibration, etc., when modeled mathematically, reduce to the matrix eigenvalue problem. Rounding errors severely limit the accuracy of the computed eigenvalues-- the conventional matrix algorithms (e.g., the ones employed by MATLAB) usually compute only the largest eigenvalues accurately. The tiny ones are lost to roundoff even though often they are accurately determined by the data and of most physical significance.

In this talk, we present a survey of recent work of the author and his collaborators on good distribution of points on a class of rectifiable sets including the sphere. We will also present some interesting applications of our work to imaging, combinatorics and numerical integration with the aim of finding new applications and collaborations. The talk will be easy to follow and undergraduate and graduate students are welcome to attend.