Apollonian packings: an application in numerical integration

Seminar: 
Group Actions and Dynamics
Event time: 
Monday, November 17, 2014 - 11:15am to 12:15pm
Location: 
205 LOM
Speaker: 
Stefan Steinerberger
Speaker affiliation: 
Yale University
Event description: 

We will discuss the problem of numerically integrating a function on the unit square [0,1]^2, describe foundational existing results and how number theory can be effectively used to attack that problem. We will then describe a curious integration method for harmonic functions based on Apollonian packings, which exploits a recent result of Kontorovich Oh to obtain a nontrivial convergence rate and propose some open problems in that direction.