Research

My research interests mainly focus on Spectral Theory, from the point of view both of Functional Analysis and of Calculus of Variations, in particular in the case of eigenvalue problems for partial differential operators.

During my Ph.D. at Università degli Studi di Padova, I studied continuity and analyticity properties for the eigenvalues of higher order differential operators (under several types of homogeneous boundary conditions), related with both equations (such as biharmonic plate problems) and systems of equations (e.g., Lamé, Reissner-Mindlin, etc.). I also obtained a few shape optimization results for these eigenvalue problems. You can find my Ph.D. Thesis here.

As a PostDoc at Politecnico di Torino I studied some properties for a class of eigenvalue problems which are related to the structural stability of suspension bridges, and reinforcements problems for plates modelling suspension bridges. I was also a member of the research project Geometrical and qualitative aspects of PDE's.

As a PostDoc at Universidade de Lisboa I studied some shape-related properties of eigenvalue problems involving the Laplace operator and others, also of higher order. I was also a member of the research project Extremal spectral quantities and related problems .

As a PostDoc at École Polytechnique Fédérale de Lausanne I studied inequalities for Riesz means and other quantities related to the eigenvalues of the Biharmonic operator.

At the moment I am studying several problems in Spectral Theory, the main ones being the properties of the eigenvalues of the Biharmonic operator with different bondary conditions, and the asymptotic properties of Riesz means for operators with discrete spectrum.

Others