Topology, Algebraic Geometry, and Dynamics Seminar (TADS): A global measure formula and logarithm law for convex real projective structures

Speaker:  Harry Bray, GMU

Title:  A global measure formula and logarithm law for convex real projective structures

Abstract:  Convex real projective manifolds with the Hilbert metric generalize hyperbolic geometry to a family of metrics with coarse hyperbolicity but low regularity; aside from the hyperbolic case, the Hilbert metric on such structures is not Riemannian and not C^2.

I will discuss how a version of the Dirichlet theorem for horoball packings can be adapted to this setting of geometrically finite Hilbert geometries which are not convex cocompact. The methods use Gromov hyperbolicity and an intrinsic definition of horoball depth. Together with a generalized global measure formula, these results imply the logarithm law for divergence of geodesics in the cusps. This is based on joint work with Giulio Tiozzo.

Time:  Friday, November 11, 2022, 1:30pm – 2:30pm

Place:  Exploratory Hall, room 4208