Intrinsic Combinatorics for the Space of Generic Complex Polynomials

Geometry Topology Seminar
Monday, September 23, 2019 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 006
Michael Dougherty – Colby College – michael.dougherty@colby.edu
Justin Lanier

The space of degree-n complex polynomials with distinct roots appears frequently and naturally throughout mathematics, but its shape and structure could be better understood. In recent and ongoing joint work with Jon McCammond, we present a deformation retraction of this space onto a simplicial complex with rich structure given by the combinatorics of noncrossing partitions. In this talk, I will describe the deformation retraction and the resulting combinatorial data associated to each generic complex polynomial. We will also discuss a helpful comment from Daan Krammer which connects our work with the ideas of Bill Thurston and his collaborators.