- Clayton Shonkwiler(Colorado State University)

- 2015.08.10, 15시

- 자연과학동(E6) Room 4415

A classical question in knot theory: given a knot type, what is the minimal number of sticks needed to build a stick knot (i.e., embedded piecewise-linear circle) of that knot type? This turns out to be rather difficult, and the answer is only known for the simplest knot types. It is helpful to dualize the question and ask: given a positive integer n, what knot types is it possible to realize with n sticks? With what frequencies do the different knot types arise? And, more generally, what is the structure of the moduli space of n-stick knots? I will give a detailed description of the geometry of this moduli space, which turns out to be a toric symplectic manifold which is a symplectic reduction of a complex Grassmannian, and give some initial results on the probability of knotted hexagons and heptagons. This geometric description also leads to algorithms for sampling stick knots thus for simulating ring polymers, which are modeled by stick knots. This is joint work with Jason Cantarella, Tetsuo Deguchi, and Erica Uehara.