Floris Vermeulen (KU Leuven)

Parametrizations in valued fields

In the o-minimal setting, parametrizations of definable sets form a key component of the Pila-Wilkie counting theorem. A similar strategy based on parametrizations was developed by Cluckers-Comte-Loeser and Cluckers-Forey-Loeser to prove an analogue of the Pila-Wilkie theorem for subanalytic sets in $p$-adic fields. In ongoing work with R. Cluckers, P. Cubides-K. and I. Halupczok, we prove the existence of parametrizations for arbitrary definable sets in Hensel minimal fields, leading to a counting theorem in this general context.