### DIMACS - Graduate Student Combinatorics Seminar

Title: A New Result In Geometric Discrepancy

Speaker: **Humberto Montalván**, Rutgers University

Date: Wednesday, April 13, 2011 12:10pm

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

Abstract:

Given n points in the unit square Schmidt showed that
there is an axis-parallel rectangle R for which the discrepancy (the
difference between the number of given points lying in R and the area
of R times n) is at least C*log(n) where C is an absolute constant. In
this talk I will give a sketch of the proof of this result. Then I
will show how to adapt Schmidt's argument to show that a fraction of
all axis-parallel rectangles have large discrepancy.

Graduate Student Combinatorics Seminars