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Elliptic Curves Associated to Two-loop Graphs

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No logo availableInstitut des Hautes Études Scientifiques (IHÉS)
 Bloch, Spencer

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Elliptic Curves Associated to Two-loop Graphs
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Amplitudes of one-loop graphs are known to be dilogarithms. What can one say about two-loop graphs? In a surprising number of cases, the motive of the second Symanzik of a two-loop graph involves (indeed, the motive is actually built around) the motive of an elliptic curve, suggesting some relation between the amplitude and elliptic polylogarithms. I will discuss a number of examples.