UAlberta-PIMS Mathematics and Statistics Colloquium: Mark Roelands

Hilbert's metric was first introduced by Hilbert, as the name suggests, in the 19th century in order to study metrics on subsets for which straight lines are geodesics. This is related to Hilbert's 4th problem. By the work of G. Birkhoff, these metric spaces can be represented on cones where the distance is determined by the partial ordering. Other than providing some historical background of Hilbert's metric, a sketch of the proof characterising the isometries on simplices will be presented which uses the cone representation.