Mathematical Structures in Feynman Integrals

Session

Session VII

Feb 15, 2023, 9:00 AM

Emmy Noether Campus

13. Elliptic substructure of 2-loop kites and 3-loop tadpoles

David Broadhurst

2/15/23, 9:00 AM

The generic 2-loop kite integral has 5 internal masses. Its
completion by a sixth propagator gives a 3-loop tadpole
whose substructure involves 12 elliptic curves. I shall show
how to compute all such kites and their tadpoles, with 200
digit precision achieved in seconds, thanks to the procedure
of the arithmetic-geometric mean for complete elliptic
integrals of the third kind. The number...

14. Computing motives: an approach to irrationality proofs for periods

Daniel Juteau

2/15/23, 10:00 AM

Following Francis Brown, I will explain why certain questions in number theory, like irrationality of zeta values, make it desirable to be able to compute some mixed Tate motives of moduli spaces. Then I will explain an algorithm devised by Clément Dupont in his Ph.D. thesis for that purpose, and its implementation in the package MotivesForBiarrangements, which uses CAP (Categories,...