Khovanskii bases in computer algebra

In this talk we will recall the definition of Khovanskii (or Sagbi) bases and compare their properties with Gröbner bases. Inspired by several applications of Gröbner bases in solving zero-dimensional polynomial systems, we present analogous applications in computer algebra using Khovanskii bases. These include an eigenvalue-based algorithm to solve equations on unirational varieties parameterized by a Khovanskii basis, as well as the implementation of a Khovanskii-based homotopy in Julia to compute linear sections of such varieties. We conclude by discussing the Mukai lifting problem for self-dual points in P^6 , which we solve by exploiting the Khovanskii-homotopy algorithm to compute linear sections on the Grassmannian Gr(2,6). The results presented are based on joint works with V. Borovik, L. Kayser, M. Panizzut and S. Telen