Organizador: César Lozano Huerta


    Jornadas de geometría algebraica en Oaxaca.

    Instituto de Matemáticas, Unidad Oaxaca.

    In a never cited paper, Brauer introduced the notion of resolvent degree to give a precise measure of the minimum complexity of any formula for the roots of a polynomial in terms of its coefficients. While the definition apparently waited until Brauer, the study of ''reduction of parameters'' dates back at least to Tschirnhaus in 1683, and, in the hands of Hermite, Klein-Burkhardt, and Hilbert was applied not only to polynomials but also to enumerative problems and modular forms. In this lecture series, I will give an introduction to the theory of resolvent degree, with a focus on applications to classical enumerative problems and the links between enumerative problems and Hilbert's conjectures surrounding his 13th problem.

    Resolvent degree, Hilbert's 13th problem and geometry

    Jesse Wolfson (University of California, Irvine)

  • 10:00am, 17 septiembre, Algebraic functions and the resolvent degree of a finite group

  • 10:00am 18 septiembre, Classical enumerative problems and the Klein-Burkhardt formula for the lines on a cubic

  • 4:00pm, 18 septiembre, Informal conversation

  • 10:00am 19 septiembre, Versal formulas and the geometry of Hilbert's 13th problem,

  • 11:30am, 19 septiembre, Informal conversation

    Work under discussion

  • Resolvent degree, Hilbert's 13th Problem and geometry (joint with Benson Farb): (arXiv)

    Relevant material

  • Lecture notes: (PDF)

  • Exercises: (PDF)