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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.