Speaker: Uri Shapira (Technion)

Title: Aspects of best approximations

Abstract:

 Any ray {tv: t>0} in Euclidean space, has a sequence of "best approximations". This sequence is a sequence of (primitive) integral vectors defined recursively by traveling along the ray and recording integral vectors whose distance to the traveler wins over distances recorded so far. In this talk I will discuss ongoing joint work with Barak Weiss in which we study natural questions about this sequence. The results I will describe split into two families: The first deals with randomly chosen rays. The second deals with rays arising from algebraic vectors. In particular, I will discuss new results regarding the sequence of determinants of best approximations.