I will present a result from some recent work-in-progress with Itay Kaplan and Pierre Simon: using the density of compressible types in NIP theories (which I talked about in a previous Oberseminar, but will recall) and some consequences of the (p,q)-theorem, we give an explicit uniform honest definition for externally definable sets \phi(A,b) where \phi is NIP, improving on previous results of Chernikov-Simon which gave the existence of such uniform honest definitions only under a global NIP hypothesis. Der Vortrag kann unter folgendem link, in Form eines Videos, besucht werden: https://www.uni-muenster.de/FB10/Service/show_article.shtml?id=7983