Algebra, Geometry, & Number Theory Seminar

The space of unimodular lattices is noncompact, and diagonal trajectories can escape to infinity in different ways. Maximal parabolic cusps distinguish these possibilities through gaps between consecutive successive minima. In this talk, I will present Hausdorff dimension formulas for divergence and divergence on average into prescribed cusps under certain diagonal flows, and discuss connections to entropy at the cusp and a quantitative form of Schmidt's conjecture.