Lille/Leuven

In the real, p-adic and motivic settings, we will present recent results on oscillatory integrals. In the reals, they are related to subanalytic functions and their Fourier transforms. In the p-adic and motivic case, there are furthermore transfer principles and applications in the Langlands program. This is joint work with Comte, Gordon, Halupczok, Loeser, Miller, Rolin, and Servi, in various combinations. 
 

I'll sketch some context for future and past research around valued fields
and motivic integration, from a model theoretic viewpoint, leaving out technical details. 
The talk will be partly conjectural.