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Day: Thursday, February 16
Time: 4:00pm
Place: BH 112
Title: Efficient travel under windy conditions
Speaker: Colleen Robles, University of Rochester
Abstract: Consider a pilot flying about the globe (2-sphere) with constant speed. In the
absence of wind, the time-efficient paths are precisely those that minimize distance –
arcs of great circles. Now imagine a wind blows across the globe. The great circles
will no longer minimize travel time.
In the first half of the talk I will describe the time-efficient flight paths -- they may be identified
with the geodesics of a Randers metric. If the wind is selected carefully, the resulting Randers
metric on the sphere will be of constant curvature K=1, and have only 2 closed geodesics.
In particular, the metric is not Riemannian. (Any given Riemannian metric on the 2-sphere has
infinitely many closed geodesics.)
In the second half of the talk I will present an extension of the problem from the globe
(the Euclidean 2-sphere) to arbitrary Riemannian manifolds, and explain why this is an interesting
problem.
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