Maximal Bounds on Cartesian Powers of Finite Graphs


May 15, 2015


Jordan Greenblatt




In the course of their work on the Unique Games Conjecture, Harrow, Kolla, and Schulman proved that the spherical maximal averaging operator on the hypercube satisfies an L2 bound independent of dimension, published in 2013. Later, Krause extended the bound to all Lp with p > 1 and, together with Kolla, we extended the dimension-free bounds to arbitrary finite cliques. We will discuss the classical and immediate contexts for these results and then outline the central ideas of their proofs. Finally, we will present subsequent results and future directions in our research program of identifying analogous asymptotics from a graph’s basic structure.


Jordan Greenblatt

Jordan Greenblatt is a PhD Student at UCLA, advised by Terry Tao. His main interests are in Harmonic Analysis, Probability and Graph Theory. For more details see