Universiteit Leiden Mathematisch Instituut
Geometry Seminar

Tuesday, 17 October 2006, 16:00 - 17:00, room 401.

Oleg Karpenkov: Multidimensional continued fractions in the sense of Klein.

Abstract:

Consider arbitrary n hyperplanes in R^n that intersect at the unique point: at the origin. The complement to these hyperplanes consists of 2^n open orthants. Consider any such orthant. The boundary of the convex hull of all integer points except the origin in the closure of the orthant is called the sail of the orthant. The set of all 2^n sails is called the (n-1)-dimensional continued fraction in the sense of Klein. I will discuss some problems and questions concerning to the face structure of the sails, and recent progress in their study.