Responsable: Francisco Jesús Castro Jiménez
Responsable actual: Francisco Jesús Castro Jiménez
Tipo de Proyecto/Ayuda: Ayudas a Consolidación de Grupos de la Junta de Andalucía
Referencia: 2008/FQM-333
Fecha de Inicio: 01-01-2009
Fecha de Finalización: 31-12-2011

Empresa/Organismo financiador/es:

• Junta de Andalucía (Consejería de Innovación, Ciencia y Empresas)

Equipo:

• Investigadores:
  • Emmanuel Briand
  • María Cruz Fernández Fernández
  • Manuel Jesús Gago Vargas
  • María Isabel Hartillo Hermoso
  • Jorge Martín Morales
  • Mercedes Helena Rosas Celis
  • José María Ucha Enríquez

Contratados:

• Investigadores:
  • Emmanuel Briand

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.