# Resolvent degree, Hilbert’s 13th Problem and geometry

```@article{Farb2020ResolventDH,
title={Resolvent degree, Hilbert’s 13th Problem and geometry},
author={Benson Farb and Jesse Wolfson},
journal={L’Enseignement Math{\'e}matique},
year={2020}
}```
• Published 11 March 2018
• Mathematics
• L’Enseignement Mathématique
We develop the theory of resolvent degree, introduced by Brauer \cite{Br} in order to study the complexity of formulas for roots of polynomials and to give a precise formulation of Hilbert's 13th Problem. We extend the context of this theory to enumerative problems in algebraic geometry, and consider it as an intrinsic invariant of a finite group. As one application of this point of view, we prove that Hilbert's 13th Problem, and his Sextic and Octic Conjectures, are equivalent to various…

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