Szemeredi's Regularity Lemma Revisited

COMPUTER SCIENCE/DISCRETE MATH, I
Topic:Szemeredi's Regularity Lemma Revisited
Speaker:Terry Tao
Affiliation:University of California, Los Angeles
Date:Monday, October 3
Time/Room:11:15am - 12:15pm/S-101

Szemeredi's regularity lemma asserts, roughly speaking, that any large dense graph can be approximated to any specified accuracy by a much simpler "finite complexity" object; it has had many applications in graph theory, combinatorial number theory, and property testing. Here we revisit the lemma from an information-theoretic perspective, and discuss a recent strengthening of the lemma in which the approximation becomes dramatically improved after adding or deleting a small number of edges to the graph. Using this stronger version one obtains a corresponding lemma for hypergraphs, which has a number of deep consequences which we will discuss.