Motivic functions, integrability, and applications to harmonic analysis on $p$-adic groups

Abstract

We provide a short and self-contained overview of the techniques based on motivic integration as they are applied in harmonic analysis on p-adic groups; our target audience is mainly representation theorists with no back- ground in model theory (and model theorists with an interest in recent ap- plications of motivic integration in representation theory, though we do not provide any representation theory background). We aim to give a fairly com- prehensive survey of the results in harmonic analysis that were proved by such techniques in the last ten years, with emphasis on the most recent techniques and applications from (13), (8), and (32, Appendix B).