04/09/2013 - 12:15pm

04/09/2013 - 1:10pm

Speaker:

Shagnik Das (UCLA)

Abstract:

The Erdos-Rademacher Theorem is a quantitative strengthening of Mantel's celebrated theorem, answering the following question: how many triangles must a graph with n vertices and n^2 / 4 + t edges have? One can ask similar questions for any extremal problem, namely how many copies of a forbidden configuration must appear once the size of a structure exceeds the extremal threshold? We study this problem for two central results in extremal set theory, Sperner's Theorem and the Erdos-Ko-Rado Theorem, answering questions of Erdos, Katona, Kleitman and West first posed some fifty years ago. This is joint work with Wenying Gan and Benny Sudakov.

Where:

Millikan 208 (Pomona College)