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Is asymptotic extremal graph theory of dense graphs trivial?

Tuesday 14th June 2011 - 14:00 to 15:00
INI Seminar Room 1
Recent developments in asymptotic extremal combinatorics have provided powerful automatic and semi-automatic methods for proving theorems in the dense setting. For example I will show how relying completely on a computer, one can solve an old conjecture of Erdos and answer a question of Sidorenko and of Jagger, Stovicek and Thomason. These new discoveries raise the following fundamental question: ``is it possible to prove every true algebraic inequalities between graph densities using a finite amount of manipulation with densities of finitely many graphs?'' Although this question itself is not well-defined, various precise refinements of it are formulated independently by Razborov and Lovasz. I will present a joint theorem with Sergey Norin which answers many of these questions.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons