Friday, January 9, 2015
12:00 pm

Theory of Computing Seminar

The Interplay Between Structure of Finite Graphs and Maximal Averages on Their Cartesian Powers
Jordan Greenblatt, UCLA


In 2013, Harrow, Kolla, and Schulman published a proof that the
spherical maximal averaging operator on the hypercube satisfies an L^2
bound independent of dimension. Later, Krause extended the bound to all
L^p with p > 1 and, together with Kolla and Schulman, we extended the
result to arbitrary finite cliques. I will provide exposition for the
classical theory and applications of maximal operators and discuss the
proof of dimension-independent bounds for clique powers/hypercubes. Then
I will talk about my current research concerning asymptotic bounds for
more general graphs. 
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