Research themes ORCID/SCOPUS Networks Thesis Books/Editing

The group SINGACOM is working on several research areas within Algebraic Geometry, Singularities, Commutative Algebra, Combinatorics, Coding, Computation and Optimization. We have specialized researchers on the several areas. The research themes include the following:

  • L1. Singularities: Classification and Resolution. Arcs and Valuations.
    • Classification of singularities and equisingularity.
    • Resolution of singularities, procedures and algorithms.
    • Arc spaces. Motivic Integration. Aplications.
    • Integral closure of ideals. Valuation spaces.
  • L2. Algebraic Geometry. Non Commutative Geometry.
    • Global Geometry of curves and of meromorphic vector fields.
    • Affine and Projective Algebraic Geometry. Toric Geometry.
    • Linear systems with assigned base conditions. Aplications to interpolation.
    • Non commutative Geometry. Homological aspects.
  • L3. Commutative Algebra. Computation. Coding.
    • Applied Algebra and Algebraic Geometry.
    • Symbolic computation in algebraic geometry and singularities.
    • Logic and computation. Algorithms complexity.
    • Algebraic-geometric codes. Coding and decoding.
  • L4. Combinatorics. Aritmetics. Optimization. Zeta Functions. PoincarĂ© Series.
    • Discrete Mathematics. Graphs.
    • Algebraic and arithmetic combinatorics. Combinatoric geometry. Optimization.
    • Local Algebra. Graduations. Valuations.
    • Zeta functions. Poincaré Series. Integration. Aplications to singularity theory.
  • L5. IMAGINARY development. Creation, visualization, innovation, culture and education.
    • Development of web IMAGINARY/es and its visual aspects.
    • Development of IMAGINARY expositions and its creative aspects.
    • Cultural innovation within IMAGINARY ambit.
    • IMAGINARY for Mathematics eduaction and for scientific training.