Abstract: Does there exist a polynomial f(X) such that all polynomials f(X), f(X)+1, f(X)+2, ..., f(X)+285 are irreducible? Clearly the answer depends on the field the coefficients are taken from.

We will discuss the connection of the above question with the twin prime conjecture. More generally we will explain the general number theoretic Schinzel hypothesis H and its quantitive version the Bateman-Horn conjecture and the corresponding analogs over finite fields. In the talk we will focus on one recent result over *large* finite fields.

Coffee will be served at 12:00 before the lecture
at Schreiber building 006