Phil Wood, University of Wisconsin, Madison

Abstract

Can you factor a random polynomial with integer coefficients into smaller factors also with integer coefficients?  Work on this simple question goes back more than 80 years, and there is still much that is not known. The talk will focus on computational work leading to a general heuristic on what the factoring behavior should be.  We will also discuss some new results on the probability of a random polynomial having factors of low degree.  Joint work with Sean O'Rourke and also joint work with Christian Borst, Evan Boyd, Claire Brekken, Samantha Solberg, and Melanie Matchett Wood