Research Group on
Mathematics and its applications
Nebrija Research Group on Mathematics and its applications Acronym: MA
Research topics
The research lines of the group are in the field of algebraic geometry and commutative algebra and their applications. Complex and real polynomials are the key objects of this topic.
1.- Symbolic methods in algebra and geometry and their applications.Symbolic computing is at the border between Mathematics and Computer Science; it seeks to analyze and solve a set of problems in commutative algebra and algebraic geometry, including their applications to other contexts, through algebraic algorithms. Specifically, we are working on:
- Algorithm in real algebraic geometry.
Key words: polynomials, systems of equations/inequations, algorithms in algebra and geometry. - Automated reasoning in euclidean geometry, implementation in GeoGebra and its applications to augmented reality, mechanisms and math education.
Palabras clave: euclidean geometry, commutative algebra, automated reasoning, dynamic geometry, augmented reality, linkages.
2.- Complex ordinary differential equations. Holomorphic foliations.Our study on complex ordinary differential equations is qualitative. Mainly, we use complex algebraic geometry techniques and analysis of several complex variables functions, which we apply to the induced foliation obtained by extending the differential equations to a complex projective variety when they are algebraic.
We are working in the following topics:
- Study of parabolic foliations: complete fields and properties of the associated derivation.
- Study of dominable varieties associated to the complete fields in the affine space.
- Exceptional values of holomorphic applications in several variables
Research Projects
Mathematical visualization: fundamentals, algorithms and applications
- File number: PID2020-113192GB-I00
- Financing institution: MCIN/AEI/ 10.13039/501100011033
- Execution Period: 01-09-2021 to 30-08-2024
Topological and Geometric Aspects in varieties
- File number: PGC2018-098321-B-I00
- Financing institution: Ministerio de Ciencia, Innovación y Universidades.
- Execution Period: 1-01-2019 to 31-12-2022
