OSU Mathematics Seminars and Colloquia
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Mon, Feb 25, 2019
Research Snapshot Seminar
3:30 PM
MSCS 509
Sphere maps and polynomials constant on a hyperplane (or line)
Jiri Lebl, Oklahoma State Unviersity.
[Abstract] [PDF]
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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