Date: 3 November ober 2017, 4:30pm
Location: Hempfield High School, Room 213
 Speaker: Vince Coll, Lehigh University
   Title: The Flat Plane

Abstract. The flat plane is very rich analytically---complex
analysis lives there.  It might appear that the plane is geometrically
uninteresting since, up to isometry, there is only one complete
metric. Even so, the plane is remarkably rich geometrically as it admits
a slew of useful incomplete metrics that arise naturally. We will show
how such metrics arise and demonstrate their utility. In particular, we
will expose a different perspective on the Uniformization Theorem for
flat Riemann surfaces, and by so doing give an alternative (and perhaps
more natural) representation of the Riemann surface for log z based on
an incomplete metric.  We will proceed to a generalization and new proof
of the Four Vertex Theorem ... and end the talk with a full
classification of flat metrics on the plane.