### DIMACS - Graduate Student Combinatorics Seminar

Title: The Combinatorics of Random Boxes

Speaker: **Linh Tran**, Rutgers University

Date: Wednesday, November 11, 2009 12:10pm

Location: Graduate Student Lounge, 7th Floor, Hill Center, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:
Consider a set of $n$ random axis parallel boxes in the unit hypercube in $\R^d$, where $d$ is fixed and $n$ tends to infinity, with some overlaps here and there. What is the most economic way to shoot all the boxes, i.e. with the minimal amount of bullets? In the talk I will show you how to attack the problem using several tools and tricks from probabilistic combinatorics. There will also be a very bold (and still
open) conjecture for someone who like a challenge!