83 citations · 326 across the 42 of their papers we have counts for
5 papers · 1 filter
Invariant measures for solvable groups and diophantine approximation
Ronggang Shi, Barak Weiss
We show that if is a line in the plane containing a badly approximable vector, then almost every point in does not admit an improvement in Dirichlet's t…
A volume estimate for the set of stable lattices
Uri Shapira, Barak Weiss
We show that in high dimensions the set of stable lattices is almost of full measure in the space of unimodular lattices.
Everything is illuminated
Samuel Lelievre, Thierry Monteil, Barak Weiss
We study geometrical properties of translation surfaces: the finite blocking property, bounded blocking property, and illumination properties. These are elementary properties which…
Dense forests and Danzer sets
Yaar Solomon, Barak Weiss
A set that intersects every convex set of volume is called a Danzer set. It is not known whether there are Danzer sets in with growth ra…
Closed orbits for the diagonal group and well-rounded lattices
Michael Levin, Uri Shapira, Barak Weiss
Curt McMullen showed that every compact orbit for the action of the diagonal group on the space of lattices contains a well-rounded lattice. We extend this to all closed orbits.