Solving equations using Khovanskii bases

Khovanskii bases extend the theory of Groebner bases of ideals in polynomial ring to general algebras. Recently they have been used to introduce exciting new methods for solving polynomial systems. We present a new eigenvalue method for solving structured polynomial equations, generilizing esatblished algorithms for toric varieties. We assume that the equations are defined on a projective algebraic variety which admits a rational parameterization by a Khovanskii basis. The talk is based on joint work with Barbara Betti and Simon Telen.