Back to Departmental Colloquium: Spring 2006
Departmental Colloquium
Date: Thursday, Mar 2, 2006
Time: 4:15PM
Location: JWB 335
Brian Conrad
Univ. of Michigan
Title |
Irreducible specialization over finite fields |
Abstract |
It is a classical and extremely difficult problem to prove theorems about prime values of irreducible polynomials over the integers. For example, it is still not known if there are infinitely many primes of the form n^2 + 1. There is a long history of analogies between the integers and polynomials (in one variable) over a finite field, and so one can formulate an analogous problem in this other setting. It turns out that there are some surprises! We illustrate the unexpected behavior by means of some simple explicit examples, and we discuss some new theorems that are used to predict such new phenomena. Finally, we discuss asymptotic results as the finite field and polynomial being specialized are allowed to vary. |
Applied Mathematics