Mathematical Physics Seminar
Thursday 20.V.2010
Time: 15:30-16:30
Room: 057
Instytut Fizyki, ul. Reymonta 4, 30-059 Kraków
Maciej
Dunajski
(University of Cambridge, UK)
Geometry of paths: from Gulliver's travels to twistor theory *)
Abstract:
A path geometry on a manifold consists of a family of curves, one curve
through every point in every direction. In 20th century cosmology and 16th
century cartography, paths arise as geodesics of a (pseudo-) Riemannian
metric.
In Penrose's twistor theory, paths correspond to points in a twistor
space.
This non-local approach has recently led to a solution of a long-standing
problem of Liouville: how to determine whether a family of curves can be
realised as geodesics of some metric.
(Please notice the exceptional time and venue this week.)
*) This will be a colloquial talk, aimed at a general audience.
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