Title: Structure of multiplicative tiling

Abstract:
Suppose Ω is a subset of the real line and A a discrete set of real numbers, both of mixed sign (else the problem is not
really new), such that A.Ω is a multiplicative tiling of the real line. In other words almost every real number can be
written uniquely as a product of an element of A and an element of Ω. When one tries to establish the structure of Ω (the
tile) and A (the set of multiples), in analogy with known facts about additive tilings, some new phenomena arise and new problems
need to be solved to achieve this goal. We show how these can be dealt with. A quick introduction to the structure of
additive tilings is necessary and will be provided for free.

Joint work with Yang Wang (Hong Kong).