[UNAM]

Organizador: César Lozano Huerta


      
      



    Jornadas de geometría algebraica en Oaxaca 2018

    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)

  • References: (DropBox)

  • Fotos: 1 2 3 4

    Relevant upcoming conference

  • Braids, Resolvent Degree and Hilbert s 13th Problem (WWW)








      
      





    Jornadas de geometría algebraica en Oaxaca 2017

    Instituto de Matemáticas, Unidad Oaxaca.

    A 19th century problem in algebraic geometry is to understand the relation between the genus and the degree of a curve in complex projective space.
    This is easy in the case of the projective plane, but becomes quite involved already in the case of three dimensional projective space.
    In this lecture series I will give an introduction to the topic, introduce stability conditions in the derived category, and explain how the two can be related. This is based on joint work in progress with Emanuele Macri.

    Derived categories and the genus of space curves

    Benjamin Schmidt (University of Texas at Austin).

  • 10:00am, 21 septiembre, Classical Results

  • 10:00am 22 septiembre, A Practical Introduction to Bridgeland Stability Conditions

  • 4:00pm, 22 septiembre, Informal conversation

  • 10:00am 23 septiembre, New Results about the Genus of Curves in Threefolds,

  • 11:30am, 23 septiembre, Informal conversation

    Expository Notes

  • Lectures on Bridgeland stability (joint with Emanuele Macri): (PDF)