Mathematics & Computer Science

Seminars and Colloquia

Friday, April 18, 2014

04:15 pm - 05:15 pm

Math Colloquium, Rich Schwartz (Brown): "Pentagrams, rational maps, and computer algebra"

Abstract: I'll describe several projectively natural iterations on the space of polygons. In each case, one starts with a polygon and produces another one by some geometric constructions involving straight lines. One of the iterations, the
pentagram map, has now been well studied and is known to be a discrete completely integrable system related to many areas of mathematics, like cluster algebras and the KdV equation. The other one, something I call the projective heat map, is sort of like a marriage of the pentagram map and heat flow. This one has a very intricate behavior and I'll describe how one can give a rigorous computer-assisted analysis of what the thing does to pentagons. The talk will
be elementary, and illustrated with computer demos.

ESC 121