Geometry is a wide field of mathematics and provides essential tools for the development of several theories inside and outside mathematics.

We are mainly concerned about the study of the singularities of maps of several complex variables defined over complex analytic varieties, therefore our research topics belong to singularity theory and intersect fields like algebraic geometry, complex analytic geometry and commutative algebra.

We study several kinds of algebraic invariants attached to maps defined over varieties, we are interested in the relation between these invariants and the effective computation of them. We also analyze the meaning of the constancy of such invariants in deformations of maps in terms of several equivalence relations of maps (for instance, topological trivialy, Whitney equisingularity and bi-Lipschitz equivalence).