Galois Groups in Enumerative Geometry and Applications

TL;DR

This paper reviews the recent resurgence of research on Galois groups in enumerative geometry, highlighting key developments, open problems, and conjectures in the field over the past 15 years.

Contribution

It provides a comprehensive overview of the modern study of Galois groups in enumerative geometry, emphasizing new directions and unresolved questions.

Findings

Recent advances in understanding Galois groups in enumerative geometry

Identification of open problems and conjectures in the field

Historical perspective on the development of the topic

Abstract

As Jordan observed in 1870, just as univariate polynomials have Galois groups, so do problems in enumerative geometry. Despite this pedigree, the study of Galois groups in enumerative geometry was dormant for a century, with a systematic study only occuring in the past 15 years. We discuss the current directions of this study, including open problems and conjectures.