The subject of this talk is the Waring problem for forms, namely, the study of higher secants of Veronese varieties.
I will show how one can obtain defining equations for examples of such varieties using Feynman/tensor diagrams
or, equivalently, the symbolic method of classical invariant theory. This hinges on finding graphs with suitable coloring properties. I will start with simple examples like binary quartics and ternary cubics and then I will report on recent joint work with Christian Ikenmeyer and Gordon Royle regarding cubics in five variables.
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