Seminar at SMU Delhi

Median spaces are metric spaces so that given any 3 points $x, y$ and $z,$ there exists a unique median point, which is a point that is on 3 geodesics between $x, y$ and $z.$ I will explain the basics on median spaces and talk about a important class of median spaces, called CAT(0) cube complexes and built using Euclidean cubes. I will explain why cocompact lattices in $SL(2,R) \times SL(2,R)$ can act properly on a median space but not on a CAT(0) cube complex. This talk will be accessible to non-specialists.