What is… a Khovanskii basis?
Vortrag von Barbara Betti
Datum: 15.04.25 Zeit: 15.45 - 16.45 Raum: ETH HG G 19.2
Gröbner bases are one of the main tools in computer algebra to solve many theoretical problems. For instance, they provide algorithms to solve the ideal membership problem, to perform elimination of variables and to solve zero-dimensional polynomial systems. In this talk, we will recall some basics notions about Gröbner bases and introduce the analogous but less known Khovanskii (or Sagbi) bases. These are particularly well-behaved sets of algebra generators that allow similar algorithms on subalgebras of the polynomial ring. Unlike Gröbner bases, Khovanskii bases are not always finite. We will discuss examples and introduce applications of Khovanskii bases to solve structured equations on projective varieties (based on joint work with M.Panizzut and S. Telen).