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math.AG2020
Tschirnhaus transformations after Hilbert
Jesse Wolfson
Let RD(n) denote the minimum d for which there exists a formula for the roots of the general degree n polynomial using only algebraic functions of d or fewer variables. In 1927, Hi…
math.AG2019
Modular functions and resolvent problems
Benson Farb, Mark Kisin, Jesse Wolfson. Appendix by Nate Harman
The link between modular functions and algebraic functions was a driving force behind the 19th century study of both. Examples include the solutions by Hermite and Klein of the qui…
math.AG2018
Resolvent degree, Hilbert's 13th Problem and geometry
Benson Farb, Jesse Wolfson
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…