Speaker: Joachim Koenig
(Technion):
Title:
2-coverable Groups and Intersective Polynomials

Abstract:
We present new theoretical results on the existence of intersective polynomials (that is, integral polynomials that have a root mod every n, but do not have a rational root) with certain prescribed Galois groups, namely the projective and affine linear groups PGL_2(#) and AGL_2(#), as well as the affine symplectic groups AGSp_4(#):=(F_#)^4#GSp_4(#). For further families of affine groups, existence results are proven conditional on the existence of certain tamely ramified Galois extensions of the rationals. We also compute explicit families of intersective polynomials with certain non-solvable Galois groups.