### DIMACS - Graduate Student Combinatorics Seminar

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.

Graduate Student Combinatorics Seminars