Sawin on Severi's Conjecture

One of my favorite questions is: for which g,n,p is the moduli space of n-pointed genus g curves Mg,n,Fp unirational/uniruled?  Will Sawin has just posted a beautiful paper on the ArXiv answering this question in most cases, for g=1.  Indeed, he shows that for np11,M1,n,Fp is not uniruled... (more below the fold)

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A "minimal" proof of the fundamental theorem of algebra

When I was in graduate school, I came up with what I think is a nice proof of the fundamental theorem of algebra.  At the time, I wrote it up here somewhat formally; I thought it might make a nice blog post, since the formal write-up obscures the very simple underlying ideas.  The goal was to use the minimal amount of technology possible -- in the end I use just a little algebra and some elementary point-set topology, as well as the implicit function theorem...

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