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Separated nets which are bounded displacement from a lattice

Alan Haynes
(University of Bristol)
Analysis Seminar
Thursday, 10 November, 2011, at 16:15-17:15, in Aud. D3 (1531-215)
A subset $Y$ of a metric space is called a separated net if there are constants $r, R>0$ such that every ball of radius $R$ intersects $Y$ and every ball of radius $r$ contains at most one point of $Y$. There is a technique in tiling theory called the `cut and project method' which provides an abundant source of separated nets. Until recently it was an open problem to determine whether separated nets coming from this method can be deformed in a uniform way onto a lattice. In this talk we will describe these ideas in more detail and explain our proof that almost all separated nets coming from the cut and project method can be translated onto a lattice by moving each point by at most some fixed constant distance. This is joint work with Barak Weiss and Michael Kelly.
Contact person: Simon Kristensen