General objectives of the project:

• Study of intrinsic properties of monoids and affine semigroups.
  • Resolution, at least partially, of problems related to the three of semigroups, the calculation  of invariants such as the conductor, gender, etc.
  • Study of non-cancellative monoids.
  • Study of the ideals in the semigroups and the varieties of Frobenius.
•  Appllications of monoids and related semigroups to the other areas of knowledge.
  • Applications to algebraic geometry.
  • Applications to the ring theory.
  • Applications to solving linear programming problems, game theory, transportation problems, economics, statistics, etc.
• Development, improvement and maintenance of scientific software. 
  • Development and maintenance of the “NumericalSgps” library in GAP, and other programs in Mathematica, Python y C++.
• Recruitment and training of new researchers.
• Organization and participation in meetings and congresses, and research stays.