Speaker: Dr. Andreas Wieser (Hebrew University of Jerusalem)

Time: 14:00-15:00  April 30, 2024 (Tuesday)

Place: MCM110

Title: Rational subspaces, shapes, and equidistribution

Abstract: Following works of Maass from the 50's and Schmidt from the 90's we study rational subspaces of Euclidean space and the shape of the integer lattice in them.

Here, we order the subspaces by height/discriminant. Conjecturally, the triples consisting of a subspace, the shape of the lattice in the subspace, and the shape in the orthogonal complement should equidistribute in the appropriate ambient space when the height goes to infinity. In this talk, we discuss the current knowledge on this conjecture based on works with Aka, Einsiedler, Luethi, Michel, and Musso. These works rely crucially on a variety of results in homogeneous dynamics.

If time permits, we will also discuss a recently discovered connection of shapes of subspaces to Gauss composition of quadratic forms and the role this connection plays in a problem from knot theory.