Generating functions and monoids in Commutative algebra with a view towards error correcting codes

Coordinator: Julio José Moyano Fernández (Universidad Jaume I de Castelló)

Members
  • Carlos Galindo Pastor (Universidad Jaume I de Castelló)
  • Olav Geil (Aalborg University)
  • Fernando Hernando Carrillo (Universidad Jaume I de Castelló)
  • Bogdan Ichim (Simion Stoilow Institute of Mathematics, Romanian Academy)
  • Francisco Monserrat Delpalillo (Universitat Politècnica de València)
  • Diego Ruano Benito (Aalborg University)
Description of the research activity
This group bases its network activity on the development and application of combinatorial techniques to commutative algebra and algebraic geometry. More specifically, we use generating functions (called Poincaré series, Hilbert series or Ehrhardt series depending on the context) which encode information about both local and global invariants of different objects, such as curve singularities, plane valuations, graded modules over polynomial rings, or Cox rings associated to surfaces. As compact expressions, those generating functions provide benefits from both a theoretical and computational point of view; this has been already shown by the implementation of many procedures in the software Normaliz, widely used for the effective treatment of affine monoids.
Our proposal relies on an important current research topic, as shown by the applicability of the required techniques as well as by the high number of recently published papers, preprints and works in progress, both in our research group and in other national and international teams. Those publications also reveal affine monoids (in particular, numerical semigroups) as actors playing an important role in the transference of results among different areas. Moreover, the discrete character of the structures appearing in our investigations seems to be really suitable for their application to the theory of error correcting codes.

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