An equisingular heritage of Bernard Teissier

TL;DR

This paper reviews Bernard Teissier's contributions to complex equisingularity theory and explores its influence in real and non-Archimedean settings, highlighting developments and legacy in the field.

Contribution

It provides a broad overview of Teissier's work and its impact on equisingularity theory across different mathematical contexts.

Findings

Development of equisingularity theory in real contexts

Extension of theory to non-Archimedean settings

Legacy of Teissier's work in modern mathematics

Abstract

We give a brief and partial overview of Bernard Teissier's work in complex equisingularity theory, and a perspective on its legacy; in particular, we focus on the development of the theory in the real and the non-Archimedean contexts. Our aim is not to go into technical details, but, hopefully, rather to give a flavour of the forms taken by these developments, while providing enough definitions and references to give the reader access to old and new reference articles in the field.