pretty thingUoP maths seminar (2015-16)

The conjugate locus

Speaker: Thomas Waters

Venue: Wednesday 21st October 2015, 2pm, LG2.04a (refreshments provided)

Abstract: Geodesics are the "straight lines" of curved surfaces, but (unlike in Euclidean space) as you follow a family of geodesics emanating from some point p in a surface the geodesics may intersect with their neighbours, or focus. The set of such focusing points is called the conjugate locus of p. The conjugate locus will generally have a certain number of cusps, and as p is moved in the surface the number of cusps may vary (for example pairs of cusps may spontaneously appear where previously there was a smooth arc); we will make a study of this process. This talk will introduce any necessary terms and makes no assumptions of previous knowledge. Also I'll use plots and animations to demonstrate what's happening.