Peter Varju - University of Cambridge Let P be a random polynomial of degree d such that the leading and constant coefficients are 1 and the rest of the coefficients are independent random variables taking the value 0 or 1 with equal probability. Odlyzko and Poonen conjectured that P is irreducible with probability tending to 1 as d grows. I will talk about an on-going joint work with Emmanuel Breuillard, in which we prove that GRH implies this conjecture. The proof is based on estimates for the mixing time of random walks on F_p, where the steps are given by the maps x-> ax and x->ax+1 with equal probability. The method may also apply to other families of polynomials.