Thursday, February 5
Milner 216, 1:00 PM
Title: An ABC inequality of heights of numbers
Abstract: The abc inequality is a remarkably simple discovery about polynomials made by Richard Mason when he was a graduate student in Cambridge circa 1982. It is perhaps best known today for inspiring the very much celebrated abc conjecture about integers by Masser and Oesterl\'e. By making use of the Mahler measure of a polynomial, it is possible to modify Mason's argument and so obtain an analogue of his abc inequality for the heights of the roots of polynomials. The technical heart of the matter is an interesting analytical inequality in harmonic analysis that may be of independent interest. We will mostly discuss Mason's inequality, the modification to heights and some simple applications.