Speaker: Martin Widmer (Royal Holloway)

Title: Rate of escape for lattices and their duals.

Abstract: For weakly admissible lattices (i.e. with no non-zero lattice points on the coordinate subspaces) the rate of escape under the action of diagonal matrices is controlled by an infimum function. We are interested in relations between this function for the lattice and for its dual lattice. It is easy to see that both functions tend to zero at the same time. Can this be made quantitative? When do we have equality? These are all linked with lattice point-counting questions. Our answers are based on work of Beresnevich's result on badly approximable points on submanifolds of R^n. This is joint work with Niclas Technau.