Title: The unexpected strength of continued fractions on the Heisenberg group
Speaker: Joseph Vandehey, University of Georgia at Athens
Seminar Type: Number Theory, Seminar Website
Abstract: Over the years, many different higher-dimensional continued fraction algorithms have been created to generalize the many useful properties of standard one-dimensional continued fractions. Last year, in joint work with A. Lukyanenko, the speaker discovered a continued fraction algorithm on the Heisenberg group that is surprisingly powerful: it appears to be the first time certain classical formulas have found higher-dimensional analogs. We will discuss these expansions, diophantine approximation, periodic continued fractions, and a number of open questions. Will include some discussion of hyperbolic geometry and ergodic theory.