Motivic integration and the Grothendieck group of pseudo-finite fields

We survey our recent work on an extension of the theory of motivic integration, called arithmetic motivic integration. We developed this theory to understand how p-adic integrals of a very general type depend on p.Comment: 11 page

Character sums associated to finite Coxeter groups

We prove a character sum identity for Coxeter arrangements which is a finite field analogue of Macdonald's conjecture proved by Opdam.Comment: 20 pages, to appear in Transactions of the A.M.

Lefschetz numbers of iterates of the monodromy and truncated arcs

We express the Lefschetz number of iterates of the monodromy of a function on a smooth complex algebraic variety in terms of the Euler characteristic of a space of truncated arcs.Comment: 10 page

Definable sets, motives and p-adic integrals

We associate canonical virtual motives to definable sets over a field of characteristic zero. We use this construction to show that very general p-adic integrals are canonically interpolated by motivic ones.Comment: 45 page