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Topology of positive zero sets of bivariate pentanomials

MSRI-UP 2017: Solving Systems of Polynomial Equations June 24, 2017 - August 06, 2017

August 04, 2017 (01:45 PM PDT - 02:20 PM PDT)
Speaker(s): Malachi Alexander (California State University-Monterey Bay), Ashley De Luna (California State Polytechnic University), Christian McRoberts (Iowa State University)
Location: MSRI: Baker Board Room
Video

Alexander, De Luna, McRoberts

Abstract

A fundamental problem in many applications is determining the real solutions of a polynomial. In recent years, the A-discriminant variety of Gelfand, Kapranov and Zelevinsky has proved to be a valuable tool. Its complement over the real numbers defines regions of coefficient values called chambers. We implement an algorithm in MATLAB that draws A-discriminant curves for families of bivariate pentanomials where the topology of the underlying zero set is constant. Our program graphs the discriminant curve with all of its chambers and automatically computes the topology of all smooth zero set for the given families of bivariate pentanomials. We hope automated topology computation for high degree polynomials will prove useful for the algebraic geometry community.

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Alexander, De Luna, McRoberts

H.264 Video Talk_5.mp4 1.53 GB video/mp4 rtsp://videos.msri.org/data/000/029/319/original/Talk_5.mp4 Download
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