Nov 3 at 17:30 in 507

Title:  Discriminants and motivic integration.

Abstract: We study invariants of a plane curve singularity  coming from motivic. integration on symmetric powers of a formal deformation of f(x,y)=0.

We show that a natural discriminant integral recovers the motivic classes of the principal Hilbert schemes of points on f(x,y)=0, while the orbifold integral gives the plethystic exponential of the motivic Igusa zeta function of f. The latter result also holds in higher dimensions. Talk is based on the joint work with Dimitri Wyss and Oscar Kivinen.

In the introductory part of the talk I am planning to discuss basics of the p-adic and motivic integration. I will also explain the statement of the monodromy conjecture that relates the poles of the Igusa function of f to the monodromy of the relevant Milnor fiber.