A Non-Archimedean Approach to Stratifications

Abstract

These are notes from a mini-course about the main results of arXiv:2206.03438: I explain how, using suitable valued fields, one obtains a natural notion of canonical stratifications (of e.g. algebraic subsets of $\mathbb{R}^n$). I also explain how the same techniques yield more invariants of singularities, and I present an application to Poincar\'e series. While some rudimentary knowledge of model theory is useful, the notes should also be accessible without such knowledge. In particular, they contain an introduction to the non-standard analysis needed for this approach.