Abstract:
In this series of informal talks I will explain my field theoretical approach towards local uniformization via a detailed study of valued function fields and the valuation theory of valued fields with residue fields of positive characteristic. I will describe the main enemy that one meets in this setting: the defect. I will explain why this is a serious obstacle not only for local uniformization, but also for a famous major problem in the model theory of valued fields. No prior knowledge on valued function fields and in model theory will be necessary, but I will assume the basics of valuation theory The audience is welcome to interrupt and ask for further explanations or divert the course of the lecture at any time.