School of Mathematical Sciences

Department Colloquium

Schreiber 006, 12:15

Brown University

I will describe a polygon iteration which starts with a polygon and does a straight line construction to produce a new one with the same number of sides. The construction is especially natural when it acts on the 2-dimensional space of pentagons modulo projective equivalence. I'll explain my theorem that the map converges almost every (class of) pentagon to the projectively regular class, except for a connected "Julia set" of planar measure 0. The highlight of my result is something like a coarse topological model for the Julia set. The talk will have a lot of computer demos in it, and it will start from scratch.

Abstract:

Coffee will be served at 12:00 before the lecture

at Schreiber building 006