Cite as: doi:10.26081/K6MW4X

**
From the softest of interactions of a magnetic field with an electron, to the
most violent collisions at the Large Hadron Collider, scattering amplitudes in
quantum field theory produce numbers and functions with interesting
number-theoretic properties. In many examples a "co-action principle" holds,
where the co-action is for a Hopf algebra acting on multiple polylogarithms.
I'll mention several arenas in which this principle can be seen at work,
including perhaps the richest set of theoretical data, scattering amplitudes in
planar N=4 super-Yang-Mills theory. Such amplitudes can in many cases be
"bootstrapped", or constructed directly from a knowledge
of the right function space of multiple polylogarithms.
**

**
**

To download: Right-click and choose "Save Link As..."

To begin viewing slides, click on the first slide below. (Or, view as pdf.)