Abstract: Classifying polynomial/rational maps of spheres leads to an
interesting combinatorial problem. In the simplest setting: if a
polynomial $p(x,y)$ of degree $d$ has $N$ positive coefficients and no
negative coefficients, and $p(x,y) = 1$
whenever $x+y=1$, then $d \leq 2N-3$. The proof leads to so-called
Newton's diagrams that can be easily drawn and analyzed. The talk
should be very accessible.
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