EVENT DETAILS AND ABSTRACT


Geometry/Physics Seminar

Title: The Geometry of Hilbert’s 13th Problem
Speaker: Jesse Wolfson
Speaker Info: UC Irvine
Brief Description: Research talk
Abstract:

Meeting ID: 922-4351-6463

Password: first word of the name of the seminar

Abstract: The goal of this talk is to explain how enumerative geometry can be used to simplify the solution of polynomials in one variable. Given a polynomial in one variable, what is the simplest formula for the roots in terms of the coefficients? Hilbert conjectured that for polynomials of degree 6,7 and 8, any formula must involve functions of at least 2, 3 and 4 variables respectively (such formulas were first constructed by Hamilton). In a little-known paper, Hilbert sketched how the 27 lines on a cubic surface should give a 4-variable solution of the general degree 9 polynomial. In this talk I’ll recall Klein and Hilbert's geometric reformulation of solving polynomials, explain the gaps in Hilbert's sketch and how we can fill these using modern methods. As a result, we obtain best-to-date upper bounds on the number of variables needed to solve a general degree n polynomial for all n, improving results of Segre and Brauer.

Date: Thursday, May 28, 2020
Time: 2:00pm
Where: Meeting ID: 922-4351-6463
Contact Person: Bahar Acu
Contact email:
Contact Phone:
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