Title: Super-Uniformity of Billiard Paths (and Planes)
Speaker: Humberto Montalvan, Rutgers University
Date: Wednesday, February 8, 2012 12:10pm
Location: Graduate Student Lounge, 7th Floor, Hill Center, Rutgers University, Busch Campus, Piscataway, NJ
Abstract:
Imagine a billiard ball traveling at unit speed in the unit square, bouncing off the walls elastically, for T seconds. Suppose that there is an irregularly shaped blob A on the surface of the table. The total length of the portions of the ball's trajectory that lie in A, divided by T, should give an approximation of the area of A.
In this talk, I will present a recent result of Jozsef Beck which essentially states that the error in this approximation is surprisingly small for a typical billiard path, regardless of the 'ugliness' of A. I will also discuss the correct way of generalizing this result to higher dimensions.