Presented by:
Spencer Bloch University of Chicago
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.
The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
