The hyperbolic Tammes problem revisited

A few weeks ago, Neil Hoffman (Oklahoma State) spoke in the Algebra, Combinatorics and Geometry seminar on a packing problem on hyperbolic surfaces that is a natural analog of the "classical" Tammes problem for packing disks on the sphere.  I will cover some of the same ground but starting at a more elementary level, introducing both problems and comparing what is known about them.  The goal is to introduce what I think are some interesting and reasonably accessible problems related to the hyperbolic Tammes problem; if time permits, I may also speculate wildly about how to solve them.