A few problems on monodromy and discriminants

TL;DR

This paper presents a list of open problems in singularity theory, focusing on classifying topological types of real function singularities and exploring Picard-Lefschetz theory, with implications for algorithmic enumeration.

Contribution

It compiles and discusses key unresolved problems related to monodromy, discriminants, and topological classifications in singularity theory.

Findings

Identification of key open problems in singularity theory

Connections between monodromy, discriminants, and topological types

Implications for algorithmic classification methods

Abstract

A problem list in singularity theory. Most of these problems are related with the algorithmic enumeration of possible topological types of non-discriminant Morsifications of real function singularities, and/or with the Picard--Lefschetz theory.