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Topology of positive zero sets of n-variate (n+4)-nomials

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

August 04, 2017 (02:30 PM PDT - 03:05 PM PDT)
Speaker(s): Davina Boykin (Valparaiso University), Sabrina Enriquez (University of Southern California), Noemi Valdez (Harvard University)
Location: MSRI: Baker Board Room

Boykin, Enriquez, Valdez


Let f be a polynomial of degree d with exactly n+4 monomial terms in R[x_1,…,x_n]. We show that one can efficiently compute an explicit polyhedral complex with the same isotopy type as the positive zero set of f. In particular, the complexity of our construction is polynomial in u + log d with high probability. Along the way, we derive and implement an algorithm that, given an n-variate (n+4)-nomial f, outputs a plot of the reduced A-discriminant contour in R^3.

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Boykin, Enriquez, Valdez

H.264 Video Talk_6.mp4 1.29 GB video/mp4 rtsp://videos.msri.org/data/000/029/320/original/Talk_6.mp4 Download
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