PhD Thesis Defence

Andrej Vukovic, Department of Pure Mathematics, University of Waterloo

"Divisibility of Discriminants of Homogeneous Polynomials"

We prove several square-divisibility results about the discriminant of homogeneous polynomials of arbitrary degree and number of variables, when certain coefficients vanish, and give characterizations for when the discriminant is divisible by p2 for p prime.

We also prove several formulas about a certain polynomial, first introduced by Bhargava, Shankar, and Wang, which behaves like an average over the partial derivatives of the discriminant. In particular, we prove that this polynomial is irreducible when d ≥ 5.

MC 5417