# Square values of polynomials

## Michael Zieve (University of Michigan)

### Thursday, April 26, 2012 4:00 pmIMS 20

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.