Last week we received a copy of the paper "The Converse of the Four Vertex Theorem" by Bjorn Dahlberg. This was originally written by Dahlberg in 1997, but he died in 1998. The paper was edited by his students, and will appear in the PAMS. A number of us are reading it and discussing it as of this moment, and so far it looks correct, and has some nice ideas in it. I'll report on it this Thursday.