Colloquium
3:00 p.m., Friday (April 11th)
Math Annex 1100
David Bao
University of Houston
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).
