Appears in collection : Model Theory and Valued Fields

I will survey the state of the long-term program initiated by T. C. Hales of making representation theory of p-adic groups “motivic” (in the sense of motivic integration), and some applications of this approach to estimates of orbital integrals, which are used in global counting problems. This is a long-term joint project with Raf Cluckers and Immanuel Halupczok