Group Seminar: DM+QMC: Uniform distribution problems on the sphere
DM+QMC: Uniform distribution problems on the sphere
Speaker: Dmitriy Bilyk (University of Minnesota)
Date: June 21, 2017 11:00
Location: SP2 416-2
We shall discuss some new results and connections between different concepts of uniform distribution of points on the sphere, such as discrepancy, energy minimization, cubature formulas and designs, uniform tessellations, almost isometric embeddings etc. A central role will be devoted to numerous recent versions, extensions, and generalizations of the so-called Stolarsky invariance principle -- an identity, which connects optimal discrepancy and energy minimizing points on the sphere. We shall also provide applications of this principle to discrepancy estimates, energy optimization, and various problems of discrete geometry. Parts of this work have been done jointly with M. Lacey, R. Matzke, and F. Dai