Nero Budur: Singularities and the monodromy conjecture

Abstract: The monodromy conjecture claims to relate different aspects of the singularities of polynomials. The conjecture is wide open in general. We give an overview of the recent results on the singularity invariants involved, such as Bernstein–Sato ideals, contact loci of arcs, together with some recently proven particular cases of the conjecture.