**UoP 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.