Presented by:
Spencer Bloch
Date:
Wednesday 29th January 2020 - 16:00 to 17:00
Venue:
INI Seminar Room 1
Abstract:
Two loop Feynman diagrams give rise to interesting cubic
hypersurfaces in n variables, where n is the number of edges. When n=3, the
cubic is obviously an elliptic curve. (In fact, a family of elliptic curves
parametrized by physical parameters like momentum and masses.) Remarkably,
elliptic curves appear also for suitable graphs with n=5 and n=7, and
conjecturally for an infinite sequence of graphs with n odd. I will describe
the algebraic geometry involved in proving this. Physically, the amplitudes
associated to one-loop graphs are known to be dilogarithms. Time permitting, I
will speculate a bit about how the presence of elliptic curves might point
toward relations between two-loop amplitudes and elliptic dilogarithms.
This is joint work with C. Doran, P. Vanhove, and M. Kerr.
This is joint work with C. Doran, P. Vanhove, and M. Kerr.
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