Colorado State University   Mathematical

The Differential Geometry of Spaces of Polygons and Polymers

By  Jason Cantarella
From  Department of Mathematics
University of Georgia
When  Monday, September 25, 2017
4:00 pm
Where  Weber 223

We are interested in understanding the geometry of the Riemannian manifold of space polygons. Applications include the study of random walks and polymers, linkages, and protein shapes. We'll start with the geometry of the space of open polygons in R^3, as this naturally models protein shapes. We identify this space with quaternionic projective space, and use the metric on HP^n to cluster some protein shapes. We will then turn to closed polygons, where we use the natural symplectic structure of closed polygon space to understand the distribution of point-to-point distances in the polygon and construct a sampling algorithm. To end the talk, we'll discuss some work in progress on making the metric structure of closed polygon space more easily visible by writing closed polygons as a quotient space (instead of a subspace) of the open polygons.

James Liu or Clayton Shonkwiler