Lior Rosenzweig: Irreducible polynomials in short "intervals".

 Knowing the Prime Number Theorem may lead to questions about counting primes in a given interval around a point x. If the size of the interval is not to small (compared to |x|), the Riemann Hypothesis predicts the answer. For shorter intervals, Goldston and Montgomery conjectured an asymptotic behaviour. In a recent paper (http://arxiv.org/abs/1204.0708), Keating and Rudnick deal with the analogous question and another similar one in arithmetic progression for irreducible polynomials in functions fields over finite fields. In the lecture we will follow their paper.