Finally, after six years of work, the preprint of my latest article with Rikard Bögvad and Boris Shapiro has been uploaded to the arXiv.
Hopefully the new mathematical tools it brings to algebraic geometry (e.g. affine Boutroux curves, the shadow of a polynomial and a generalized polar derivative) will prove to be very useful in the future.
Tl;dr, cool stuff happens to the zeros of a polynomial when you raise it to some integer power n and then differentiate it m times. See figures 2 and 3 in the article. Subsections 7.3 and 7.4 will probably be of interest to moderate math nerds here, too.
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