Discrete Curvatures, Least Squares Error and the “Quantitative Geometry” of Measures

Seminar: 
Analysis
Event time: 
Wednesday, October 8, 2008 - 10:45am to 11:45am
Location: 
215 LOM
Speaker: 
Tyler Whitehouse
Speaker affiliation: 
University of Minnesota
Event description: 

We introduce some discrete curvatures for simplices based on multi-way generalizations of the ordinary sine function, and we show how their integrals can be used to estimate various least squares errors for measures on Euclidean spaces. In addition, we relate these estimates to a quantication of the types of simplices that can be constructed in the support of the measure.