Flag algebras provide a method, recently developed by Razborov, designed for attacking
problems in extremal graph theory. There are recent applications of the method
also in discrete geometry or permutation patterns. The aim of talk is to give a gentle
introduction to the method and show some of its applications to hypercubes and permutations.
The talk is based on joint work with J. Balogh, P. Hu, H. Liu, O. Pikhurko, B. Udvari, and J. Volec.