Abstract
We present a review of how ideas inspired by recent developments in number theory find applications in physics in the context of scattering amplitudes and Feynman integrals. In particular, we show how one can combine (and conjecturally extend) Goncharov's Hopf algebra on multiple polylogarithms by recent results by Brown on motivic multiple zeta values. These results can be used to derive in an effective way complicated relations among multiple polylogarithms. We conclude by illustrating the use of these concepts in various contexts related to the computation of scattering amplitudes and Feynman integrals.
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