Calendar

The ends of finite-volume hyperbolic (n+1)-manifolds are cusps of the form B x R+ for some compact, flat n-manifold B.  In 2009, McReynolds built on work on Long and Reid to prove that every such n-manifold arises as the cusp cross section of some hyperbolic (n+1)-manifold using an arithmetic construction.  A natural further question to ask is under what conditions each cross-section can arise.  In this talk, we give an algebraic condition that describes exactly when a given flat manifold arises (as a cusp cross-section) in a commensurability class of cusped arithmetic hyperbolic manifolds.  Time permitting, we will also discuss some applications, including a potential new way to prove a hyperbolic manifold is non-arithmetic.  This is joint work with Duncan McCoy.

These lectures will describe connections between dynamical systems and topics including algebraic geometry, number theory,
unipotent flows and fractal Jordan curves.

All talks will be for a general audience, and no talk is a prerequisite for any other.