Date: Wednesday, 15.10, 14:15–15:00

Speaker: Olivier Verdier, Umeå, Sweden

Title: Relations of geometric integration to computer science and physics

Abstract:

I’ll present two recent results which witness interesting connections between numerical integration and computer science, and between numerical integration and physics.

A numerical integrator is a method to numerically solve a differential equation. We recently characterised the integrators which are independent of the choice of origin, axes, and units. It turns out that this characterisation has a parallel with parametric type polymorphism, a powerful technique to make sure an implementation satisfies certain specifications.

For the connection with physics, we examine spin systems. These model for instance hurricanes on gas planets, or interacting black holes. They can be seen as mechanical systems where the phase space is a product of spheres. We present an extremely simple numerical method which is the pendant of the midpoint rule for linear phase spaces.

The talk will be elementary and no prerequisite knowledge is necessary.

 

The slides can be found here: http://www.olivierverdier.com/s/hib-2014-10