Geometric Group Theory Seminar - Anton Lukyanenko

Title: Diophantine approximation in the Heisenberg group

Speaker: Anton Lukyanenko (University of Michigan)

Abstract: The Heisenberg group arises both as a simple example of a nilpotent Lie group, and as the boundary of complex hyperbolic space. Studying it from the geometry-of-numbers perspective, we ask how well a generic point can be approximated by a rational point. Surprisingly, we obtain two natural ways make the question precise. The resulting Carnot Diophantine approximation applies to a broader class of nilpotent groups, while Siegel Diophantine approximation is directly related to complex hyperbolic geometry. This is joint work with Joseph Vandehey.

Seminar URL: https://research.math.osu.edu/ggt/