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Thursday, December 18, 2014

**Abstract:** An important conjecture of Erdos-Simonovits and Sidorenko states that if $H$ is a fixed bipartite graph, then the random $n$-vertex graph ($n$ is large) has asymptotically the minimum number of copies of $H$ over all graphs of the same order and edge density. This conjecture also has an equivalent analytic form and has connections to a broad range of topics such as matrix theory, Markov chains, graph limits, and quasirandomness. In this talk, I will provide an overview on this beautiful conjecture and discuss some recent results. Joint w/ Jeong Han Kim (KIAS) and Joonkyung Lee (Oxford).