UoP maths seminar (2013-14)
Surfaces with regular geodesics.
Speaker: Thomas Waters
Venue: Wednesday 5th February 2014, 2pm, LG2.04a (refreshments provided)
Abstract: Geodesics are a special class of curves in a surface which locally minimize length; as such they are the "straight lines" of a surface. The notion generalises nicely to higher dimensional surfaces (manifolds) and an interesting question is: for what surfaces are the geodesics regular and well-behaved, and for what surfaces are the geodesics irregular and chaotic? This is made precise with the concept of integrability and in this talk I will discuss ongoing work which attempts to construct surfaces whose geodesic equations are integrable. The talk aims to be informal and I hope to introduce all the relevant terms from scratch to suit a general audience.