Generalized analytic functions are locally defined as the sum of a convergent power series whose support is contained in the product of well-ordered subsets of non-negative real numbers (i.e., the generalized power series considered by L. van den Dries and P. Speissegger in their seminal paper on this topic).

In 2013, R. Martín Villaverde, J.-P. Rolin and F. Sanz Sánchez proved the local uniformization for this class of functions, introducing first the category of generalized analytic manifolds (topological manifolds with boundary and corners endowed with a generalized analytic structure). Since then, it has been open the problem about the Global Resolution of Singularities of generalized analytic functions. We will see a result that gives a partial answer in this direction. Namely, we will prove that any generalized analytic function can be globally transformed to a function whose generalized-analytic components are monomials with respect to suitable local coordinates, by means of a finite sequence of global blowing-ups.

This talk is based on joint work with Beatriz Molina Samper and Fernando Sanz Sánchez.