Séminaire OrléansCovering the plane by rotations of a lattice arrangement of disks
Thursday 24 May 2007 15:00 - Orléans - Salle S104 (Bât Sciences)
Suppose we put an $\epsilon$-disk around each lattice point in the plane, and then we rotate this object around the origin for a set $\Theta$ of angles. When do we cover the whole plane, except for a neighborhood of the origin? It is very easy to see that if $\Theta = [0,2\pi]$ then we do indeed cover. The problem becomes more interesting if we try to achieve covering with a small closed set $\Theta$. Fourier-analytic and elementary arguments yield various results. This is joint work with M. N. Kolountzakis and A. Iosevich.