What do I work on?

• My research has its starting point in the intersection of algebraic combinatorics and representation theory and expands to other areas from there. For instance, the symmetric functions as a way to understand character theory for the symmetric group and the general linear group, the combinatorial properties of different orders on permutations as tools to describe the multiplication of the Schubert classes in the cohomology ring of the Grassmannian, or the invariants in the shuffle algebra that give us the description of the invariants for multidimensional series in stochastic analysis. Arising from other areas, these problems involve combinatorial objects and structures that I want to study. 

• I am interested in symmetric polynomials from a combinatorial point of view. More precisely, I study symmetric polynomials appearing in other areas trying to understand the combinatorial objects that encode them. For instance, I have worked on Macdonald polynomials and their specializations and I am currently working on understanding the multiplication of Schubert polynomials and the e-positivity of the chromatic polynomials. Moreover, I'm interested in the structural constants that come from representation theory, such as the Kronecker coefficients or the plethysm coefficients. 

• I have also worked on signatures of paths and their relation with the shuffle algebras, and on an insertion algorithm for diagrams algebras.