|Date: Wednesday, September 26, 2012
Location: 4096 East Hall (4:10 PM to 5:00 PM)
Title: Random points and lattice points in convex bodies
Abstract: Assume K is a convex body in R^d and X is a (large) finite subset of K. How many convex polytopes are there whose vertices belong to X? Is there a typical shape of such polytopes? How well does the maximal such polytope (which is actually the convex hull of X) approximate K? In this lecture I will talk about these questions mainly in two cases. The first is when X is a random sample of n uniform, independent points from K. In this case motivation comes from Sylvester's famous four-point problem and from the theory of random polytopes. The second case is when X is the set of lattice points contained in K and the questions come from integer programming and geometry of numbers. Surprisingly (or not so surprisingly), the answers in the two cases are rather similar.
Speaker: Imre Barany
Institution: University College, London