Speakers

Carlos D'Andrea

Elimination Theory

  • Algebraic and Geometric Elimination
  • The Elimination Theorem
  • Resultants and Elimination
  • Classical and Modern Resultants
  • Computational Tools

Ignacio García Marco

Semigroups and its interactions with toric ideals and discrete structures

  • Numerical semigroups
  • 1-dimensional toric ideals
  • The poset of a numerical semigroup: Möbius function and chomp on semigroups
  • Noncommutative semigroups: Cayley posets

Viktor Levandovskyy

Computing in finitely presented algebras with Letterplace

  • Theory of Groebner bases of two-sided ideals over the free associative algebra over a field

    Monomial orderings, division procedure, normal form. Generalized Buchberger's algorithm. Homogeneous and inhomogeneous input. Truncated finite Groebner bases. Tame and wild infinite Groebner bases.

  • Letterplace technique for computing Groebner bases of two-sided ideals

    Letterplace correspondence of monomials, orderings and Groebner bases.

    Practice: First experience with the Singular extension called Singular:Letterplace

  • Applications of noncommutative Groebner bases

    Determining the explicit form of the canonical (wrt a fixed monomial ordering) K-basis of a finitely presented algebra. Algebras of linear partial operators. Computations of K-dimension, Gelfand-Kirillov dimension and an upper bound of the global homological dimension. Establishing Noetherian, prime and semiprime properties.

    Practice: Working with Letterplace libraries fpadim.lib and fpaprops.lib