Résumé : I will introduce in this talk the combinatorial Connes-Kreimer Hopf algebra of Feynman graphs, celebrated structure known to encode the combinatorics of renormalization in quantum field theory (QFT). Hochschild cocyles (associated to some particular graphs) will then be defined; this allows to write down the combinatorial Dyson-Schwinger equations (recursive equations in power series written in terms of these Hochschild cocyles). It is worth emphasizing that the Dyson-Schwinger equations can play a crucial role in non-perturbative QFTs. Several explicit examples will be given to illustrate these various notions. Based on: http://arxiv.org/abs/0907.2182
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