Seminar Details
2006-12-14 (16.30pm) : Colloquium CESAME/MAPA "Geometric Knot theory"
At Auditoire Euler
Organized by Mathematical Engineering
Speaker :
John Sullivan (T.U. Berlin)
Abstract :
Geometric knot theory is the study of geometric properties of
space curves that derive from their topological knottedness.
Perhaps the most famous result is the Fary/Milnor theorem relating
total curvature to bridge number, but the field can be dated back
to work of Pannwitz on quadrisecant lines for knots. There has been
a surge of interest in geometric knot theory over the past decade,
partly due to biophysical applications to the shapes of knotted
polymers like DNA molecules. One interesting problem with some
surprising answers asks for the shapes of knots and links tied
tight in rope of fixed thickness. We will survey recent results on
this so-called ropelength problem, as well as some new strengthened
versions of the theorems of Pannwitz and Fary/Milnor.