Are Riemannian metrics adequate on windy days?

Imagine navigating on a Riemannian landscape (M,h) such as a Euclidean lake or a spheroidal atmosphere, under the influence of a mild wind W. With the wind present, the most efficient paths are no longer the geodesics of the Riemannian metric h. Instead, they are the geodesics of a Finsler metric. The concept of sectional curvatures in Riemannian geometry admits a fruitful generalisation to Finsler geometry. This is the notion of flag curvatures. A ubiquitous class of metrics with constant flag curvature is described by some system of nonlinear partial differential equations.

The navigation picture effects a complete classification of the solutions. Isometry classes of such solutions are counted by Lie theory.

Refreshments will be served at 2:45 p.m. in the Faculty Lounge, Math Annex (Room 1115).