M / E28

The problem of expressing a homogeneous polynomial as a sum of powers of linear forms is very classical and goes back to the work of Sylvester, Hilbert, and Scorza among others. The real rank of a homogeneous polynomial is the smallest number of linear real forms such that the polynomial admits such a representation. The space parametrizing all real decompositions of a polynomial as a minimal sum of powers is a semialgebraic set sitting inside the classical varieties of sums of powers. We will discuss these real geometric objects for general plane curves of small degrees. This is a joint work with M. Michalek, H. Moon and B. Sturmfels.

Dr. Emanuele Ventura

MPI Leipzig