Time: 14:30
Speaker: Yan Xu (Dongbei University of Finance and Economics)
Title: "The ubiquitous B-splines from approximation to Combinatorics: Eulerian numbers, polytopes and Askey scheme"
Room: MC 108

Abstract: Spline functions are original derived from approximation theory then were applied to established the theory of wavelets which is the most important tool in CAGD founded by engineers at the first beginning. They are also closely related with some branches in pure mathematics, such as Combinatorics and Asymptotic analysis. Due to the somewhat high distance between these fields, people working in Enumerative Combinatorics, Partition functions and Asymptotic analysis of biorthogonal systems do not seem to be fully aware of the results on the B-splines. This presentation may shed some lights on the connection between the related problems arising in different fields such as B-splines and Eulerian polynomials, Box-spline and the volume of polytopes, the asymptotic properties of splines and Askey scheme. It may useful to bring together some areas of research which have developed independently without much knowledge of each other.