Speaker: 

Jiri (George) Lebl, http://math.okstate.edu/people/lebl/ or http://www.jirka.org/

A classical problem in complex variables (both one and several) is the classification of proper mappings between two given domains.  A special and well-studied case is the case of balls, as balls have lots of symmetry and admit many such maps.  It is a curious problem that has led to both very deep and difficult papers on one hand and undergraduate research on the other.  I will go over some of the basic results in this area, including some recent results, and leave a few open questions.  Recently I, together with two of my students, have been studying the closely related case of proper mappings between annuli (ball minus a smaller ball), and we have made some interesting progress that I will also mention.  The talk will be accessible to a wide audience.