Student Dynamics Seminar

Properly convex subsets of projective spaces carry a natural Finsler metric called the Hilbert metric (defined using affine charts). The resulting geometries are called Hilbert geometries. Prominent examples include the Beltrami-Klein model of the hyperbolic space and symmetric spaces (with a geometry that is vastly different from the standard Riemannian one).

Yves Benoist studied divisible Hilbert geometries (that is, admitting compact quotient) and proved that subject to the assumption of strict convexity, Hilbert geometries have properties reminiscent of Riemannian negative curvature (Anosov geodesic flow, properties of closed geodesics, etc.). The talk will be based on a part of Benoist's paper 'Convexes divisibles I'. This will be the first talk of a series of talks and hence, will not assume any prior knowledge of the area.
Speaker(s): Mitul Islam (UM)