Some Advances in Sidorenko’s Conjecture
Joonkyung Lee
University of Oxford, UK
University of Oxford, UK
2014/09/04 *Thursday* 4PM-5PM
Room 1409
Room 1409
Sidorenko’s conjecture states that for every bipartite graph 
on 
\begin{eqnarray*}
\int \prod_{(i,j)\in E(H)} h(x_i, y_j) d\mu^{|V(H)|}
\ge \left( \int h(x,y) \,d\mu^2 \right)^{|E(H)|}
\end{eqnarray*}
holds, where
is the Lebesgue measure on ![[0,1]](https://s0.wp.com/latex.php?latex=%5B0%2C1%5D&bg=ffffff&fg=000000&s=0 "[0,1]")
and 
is a bounded, non-negative, symmetric, measurable function on ![[0,1]^2](https://s0.wp.com/latex.php?latex=%5B0%2C1%5D%5E2&bg=ffffff&fg=000000&s=0 "[0,1]^2")
. An equivalent discrete form of the conjecture is that the number of homomorphisms from a bipartite graph to a graph 
is asymptotically at least the expected number of homomorphisms from to the Erdos-Renyi random graph with the same expected edge density as . In this talk, we will give an overview on known results and new approaches to attack Sidorenko’s conjecture.
This is a joint work with Jeong Han Kim and Choongbum Lee.
on \begin{eqnarray*}
\int \prod_{(i,j)\in E(H)} h(x_i, y_j) d\mu^{|V(H)|}
\ge \left( \int h(x,y) \,d\mu^2 \right)^{|E(H)|}
\end{eqnarray*}
holds, where
is the Lebesgue measure on and is a bounded, non-negative, symmetric, measurable function on . An equivalent discrete form of the conjecture is that the number of homomorphisms from a bipartite graph to a graph is asymptotically at least the expected number of homomorphisms from to the Erdos-Renyi random graph with the same expected edge density as . In this talk, we will give an overview on known results and new approaches to attack Sidorenko’s conjecture.This is a joint work with Jeong Han Kim and Choongbum Lee.