Theory of Computing Seminar
Annenberg 213
The Interplay Between Structure of Finite Graphs and Maximal Averages on Their Cartesian Powers
Jordan Greenblatt,
UCLA,
Abstract:
In 2013, Harrow, Kolla, and Schulman published a proof that the
spherical maximal averaging operator on the hypercube satisfies an L2
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.
spherical maximal averaging operator on the hypercube satisfies an L2
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.
For more information, please contact Thomas Vidick by email at [email protected].
Event Series
Theory of Computing Seminar Series