Pure Mathematics Colloquium - Gauss-Kuzmin statistics for faces of Klein polyhedra

Speaker:   Oleg Karpenkov (University of Liverpool)

Title:     Gauss-Kuzmin statistics for faces of Klein polyhedra

Abstract:

In this talk we consider multidimensional geometric continued fractions in the sense of Klein, which is an alternative approach to Jacobi-Perron continued fraction algorithms. Klein continued fractions are certain surfaces equipped with polyhedral structure. In the algebraic case the polyhedral structure has a periodic nature. We show several examples of multidimensional continued fractions and explain how to use Mobius geometry to gen- eralize Gauss-Kuzmin ergodic statistics from the case of ordinary continued fractions to the multidimensional case.