# Virtually all polynomials are irreducible

Seminar

Speaker

Prof. Lior Bary-Soroker (Tel Aviv University)

Date

16/01/2019 - 11:00 - 10:00Add to Calendar

`2019-01-16 10:00:00``2019-01-16 11:00:00``Virtually all polynomials are irreducible``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 in whether the same holds when one considers sparse families of polynomials—notably, polynomials with plus-minus 1 coefficients. In particular, “some guy on the street” conjectures that the probability for a random plus-minus 1 coefficient polynomial to be irreducible tends to 1 as the degree tends to infinity (a much earlier conjecture of Odlyzko-Poonen is about the 0-1 coefficients model) . In this talk, I will discuss these types of problems, their connection with analytic number theory.``Third floor seminar room (room 201, building 216)``אוניברסיטת בר-אילן - Department of Mathematics``mathoffice@math.biu.ac.il``Asia/Jerusalem``public`Place

Third floor seminar room (room 201, building 216)

Abstract

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 in whether the same holds when one considers sparse families of polynomials—notably, polynomials with plus-minus 1 coefficients.

In particular, “some guy on the street” conjectures that the probability for a random plus-minus 1 coefficient polynomial to be irreducible tends to 1 as the degree tends to infinity

(a much earlier conjecture of Odlyzko-Poonen is about the 0-1 coefficients model) . In this talk, I will discuss these types of problems, their connection with analytic number theory.

Last Updated Date : 06/01/2019