Chromatic properties of graphs and the Waring problem for homogeneous polynomials

Abdelmalek Abdesselam
University of Virginia

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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