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 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.