Abstract
For any given graph $H$, one may define a natural corresponding functional $\|.\|_H$ for real(or complex) valued functions by using the homomorphism density of $H$. We say that $H$ is \emph{norming} if $\|.\|_H$ is a norm. This generalises the Gowers octahedral norms, a widely used tool in extremal combinatorics to quantify quasirandomness.
In 2008, Lov\'{a}sz asked what graphs are norming. This has been a central question in the theory of dense graph limits and also connects to Sidorenko's conjecture, a major open problem in extremal graph theory.
For the recent few years, there have been interesting developments on the Lovász question, where algebraic combinatorics, extremal graph theory and functional analysis meet. In this talk, I will discuss some of the progress.
Based on joint work with David Conlon, Frederik Garbe, Jan Hladk\'{y}, Bjarne Sch\"{u}lke, and Sasha Sidorenko.