Rothschild Lecture: Elliptic curves associated to two-loop graphs (Feynman diagrams)
1 hour 6 mins,
973.64 MB,
MPEG-4 Video
640x360,
30.0 fps,
44100 Hz,
1.96 Mbits/sec
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Description: |
Bloch, S
Wednesday 29th January 2020 - 16:00 to 17:00 |
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Created: | 2020-01-30 09:19 |
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Collection: | K-theory, algebraic cycles and motivic homotopy theory |
Publisher: | Isaac Newton Institute |
Copyright: | Bloch, S |
Language: | eng (English) |
Distribution: | World (downloadable) |
Explicit content: | No |
Aspect Ratio: | 16:9 |
Screencast: | No |
Bumper: | UCS Default |
Trailer: | UCS Default |
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. |
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