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)