Square values of polynomials
Michael Zieve (University of Michigan)
Thursday, April 26, 2012
Let $f(x)$ be a polynomial whose coefficients are
rational numbers. I will discuss the question: for how many
rational numbers $c$ is $f(c)$ the square of a rational number?
Along the way, I will present several important results and
conjectures in number theory and arithmetic geometry, including
theorems of Minkowski, Mazur, Faltings, and Bhargava–Shankar,
and conjectures of Bombieri–Lang and Birch–Swinnerton-Dyer.
Comments: Special Colloquium for Awards Day.