Dr. Jason Parsley, 4 December, 2006
  The Linking, Twisting, and Writhing of Curves

Abstract:   In this talk, we'll consider simple closed curves in three-dimensional space.  If you have two curves, can you pull them apart from each other?  If not, they are said to be "linked", and we define an integer that measures their amount of "linking".

A diver twists when she rotates about an axis from head to toe. Similarly, we say a piece of rope twists when it rotates about its core axis.  We'll talk about how to define the twist of a curve.  We need one more concept:  the writhe of a curve measures how much the curve wraps and coils around itself -- think of a tangled telephone cord.

In 1962, the Romanian mathematician Calugareanu related these three ideas by showing that LINK = TWIST + WRITHE.  We will demonstrate this, discuss the fine print underlying this statement, and extend it to current research.


Biographical sketch:   Jason Parsley holds a bachelor's degree in mechanical engineering from Duke University and did his graduate work in mathematics at Penn.  His mathematical interests combine differential geometry, topology, analysis, and physics.  He is especially drawn to problems concerning curves or (3-d) vector fields.  Before joining Wake Forest this fall, he was most recently a postdoc at the University of Georgia.  His other interests include tennis, basketball, film, and driving cross-country, which he will do for the seventh time this December.