Responsable: Francisco Jesús Castro Jiménez
Tipo de Proyecto/Ayuda: Plan Nacional del 2010
Referencia: MTM2010-19336
Fecha de Inicio: 01-01-2011
Fecha de Finalización: 31-12-2014

Empresa/Organismo financiador/es:

• Ministerio de Ciencia e Innovación

Equipo:

• Investigadores:
  • Emmanuel Briand
  • Manuel Ceballos González
  • María Cruz Fernández Fernández
  • Manuel Jesús Gago Vargas
  • Michel Granger
  • María Isabel Hartillo Hermoso
  • Herwig Hauser
  • Juan Núñez Valdés
  • Mercedes Helena Rosas Celis
  • Nobuki Takayama
  • José María Ucha Enríquez
• Personal Investigador en Formación:
  • Laura Colmenarejo Hernando (alta: 02/01/2012)

Contratados:

• Investigadores:
  • Alberto José Armenta Berregui
  • Manuel Ceballos González
  • Sebastián López Cano
• Técnicos/Personal Administrativo:
  • María Helena Cobo Pablos
  • Jorge Miguel García García
  • Carlos González Rivero
  • Haydee Jiménez Tafur
  • Rafael Ruiz León
  • Alberto Solís Encina
  • Angélica Marcela Torres Bustos

Resumen del proyecto:

Research objectives

1. D-modules (Logarithmic D-modules and hypergeometric D-modules).
Duality for logarithmic D-modules and the range of validity of the logarithmic comparison theorem for quasi-free divisors. Computing the solutions (classical and higher order solutions) of Gevrey type of irregular hypergeometric D-modules (including GKZ modified systems). The study of the behavior of the holomorphic solutions of hypergeometric systems when moving from a generic parameter to a special one and the other way round.

2. Combinatorial representation and invariant theory.
The study of the Kronecker coefficients of the representation theory of the symmetric group, and specially the research of explicit formulas for them in function of their labels. The study of the Reduced Kronecker Coefficients and their various interpretations.

3. Computational Methods in Lie Algebras.
The computation of the dimension of a maximal abelian subalgebra of a complex Lie algebra of finite dimension and similarly for the Weyl algebra.

4. Computational Methods in (Non Linear) Integer Programming.
Study of integer optimization problems using algebraic tools based on Groebner bases, with linear and non-linear constraints, such as portfolio management with different risk functions, or reliability systems. The sensitivity of the solutions may be analyzed by using Groebner fan theory, and some multi-objective problems are treated.