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}
}
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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