It has been known for almost a hundred years that most polynomials with

integral coefficients are irreducible and have a big Galois group. For

a few dozen years, people have been interested whether the same holds

when one considers sparse families of polynomials — notably, polynomials

with ±1 coefficients. In particular, it was conjectured

that the probability for a random ±1 coefficient polynomial to be

irreducible tends to 1 as the degree tends to infinity. In this talk, I

will discuss these types of problems, some approaches to attack them, and I

will present some new results toward the conjecture, joint with Gady Kozma.

### Galois Seminar

Friday, February 2, 2018 - 3:15pm

#### Lior Bary-Soroker

Tel Aviv University and Montreal