Connes-Kreimer algebraic structures in field theory and quantum gravity

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The concept of renormalization lies at the heart of fundamental physics. I introduce in this talk the Connes-Kreimer algebraic approach for expressing renormalizability in quantum field theories as well as the extension of these notions to the manifestly non-local framework of noncommutative quantum field theories. Finally, I will present an attempt to further generalize these concepts to quantum gravity models. based on: 0909.5631 [gr-qc], Class. Quant. Grav. (in press)