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:
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: