Mathematics Colloquia and Seminars

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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 a putative minimizer is legitimate.