Rutgers Discrete Mathematics Seminar

Title: Nikodym Sets in Finite Fields

Speaker: Swastik Kopparty, Rutgers University

Date: Tuesday, April 8, 2014 2:00pm

Location: Hill Center, Room 525, Rutgers University, Busch Campus, Piscataway, NJ


A Nikodym set in F^n (where F is a finite field), is a subset N of F^n such that for every point x in F^n, there is some line L through x such that all of L (except possibly x) is contained in N. The basic problem is to determine how small a Nikodym set can be. Nikodym sets are closely related to Kakeya sets, but there are some curious differences. I will survey what theorems are known about Nikodym sets, and prove some of them.