DIFFERENTIAL GEOMETRY/PDE SEMINAR

Thursday, April 15, 2004 Padelford C-36 1:30 pm Criticality for ropelength of knots and links

Rob Kusner

(University of Massachusetts, Amherst and MSRI)

We consider the problem of finding the shapes of tightly knotted or linked ropes (tubes of uniform thickness around embedded curves in 3-space). We will review recent work on minimization of ropelength (the ratio of length over thickness) within an isotopy class, especially its relation to classical invariants such as crossing number, bridge number and various generalizations. Then we will discuss a critical point theory for length of knotted or linked curves subject to a thickness constraint. This leads to a ”balance of forces” criterion which characterizes critical configurations, and in particular, which lets us decide whether or not a putative minimizer is legitimate.

For more information about this seminar, visit the DG/PDE Seminar Web page (from the Math Department home page, www.math.washington.edu, follow the link Seminars, Colloquia, and Conferences).

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