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UID:2019082305543320190828T16000020190828T1650005d6028595d631@uic.edu
CATEGORIES:MEETING
STATUS:TENTATIVE
DTSTAMP:20190823T114733
DTSTART:20190828T160000
DTEND:20190828T165000
SUMMARY:Algebraic Geometry Seminar: The Geometry of Hilbert's 13th problem, by Jesse Wolfson
DESCRIPTION:Jesse Wolfson (University of California Irvine): The Geometry of Hilbert's 13th problem Given a polynomial x^n+a_1x^{n-1}+ . . . + a_n, what is the simplest formula for the roots in terms of the coefficients a_1, . . . a_n? Following Abel, we can no longer take simplest to mean in radicals, but we could ask for a solution using only 1 or 2 or d-variable functions. Hilbert conjectured that for degrees 6,7 and 8, we need 2,3 and 4 variable functions respectively. In a too little known paper, he then sketched how the 27 lines on a cubic surface should give a 4-variable solution of the general degree 9. In this talk, Ill review the geometry of solving polynomials, explain Hilberts idea, and then extend his geometric methods to get best-to-date upper bounds on the number of variables needed to solve a general degree n polynomial. Please click here to make changes to, or delete, this seminar announcement.
LOCATION:427 SEO Chicago IL
CLASS:PRIVATE
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