Research themes ORCID/SCOPUS Networks Thesis Books/Editing Videos

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. Interpolation and algebraic-geometric fitting.
    • Non commutative Geometry. Homological aspects.
  • L3. Commutative Algebra. Computational Algebra. Coding.
    • Applied commutatice Geometric Algebra.
    • Computational Algebra and Algebraic Geometry.
    • Tropical Geometry. Intersection computation.
    • Algebraic-geometric codes. Classical, quantum and network Coding. Decoding.
  • L4. Combinatorics. Aritmetics. Optimization. Zeta Functions. PoincarĂ© Series.
    • Discrete Mathematics. Graphs. Topology
    • Algebraic and arithmetic combinatorics. Combinatoric geometry. Optimization.
    • Local Algebra. Graduations. Filtrations.
    • Zeta functions. Poincaré Series. Integration. Aplications to singularity theory.
  • L5. Computation. Algorithms. Prediction. Visualization.
    • Sybolic computation in Algebraic Geometry and Singularities.
    • Algorithms. Logic and Complexity.
    • Mathematical models in Geosciences. Predictive studies.
    • Development of web IMAGINARY/es. Creative aspects. Cultural Innovation.