Quadratic Forms on Graphs

COMPUTER SCIENCE/DISCRETE MATH SEMINAR, II
Topic:Quadratic Forms on Graphs
Speaker:Konstantin Makarychev
Affiliation:Princeton University
Date:Tuesday, February 22
Time/Room:10:30am - 12:30pm/S-101

We introduce a new graph parameter, called the rothendieck constant of a graph. This parameter is a generalization of the classical Grothendieck constant; and it is equal to an integrality gap of a certain SDP problem, which has various algorithmic applications. Our results improve a recent result of Kashin and Szarek on Gram matrices of uniformly bounded functions, and settle a problem of Megretski and of Charikar and Wirth. Noga Alon described the motivation of the problem and our results at the members seminar on Monday, Jan 31. In my talk, I will give proofs of these results.