Sesión Ecuaciones Diferenciales y aplicacionesEigenvalue curves for Dirac operators: a strategy for shape optimization
Tomás Sanz-Perela
Universitat de Barcelona, España - Esta dirección de correo electrónico está siendo protegida contra los robots de spam. Necesita tener JavaScript habilitado para poder verlo.
In this talk, I will present a shape optimization problem for a Dirac operator and a strategy to approach it, both in the 2D and 3D settings. It consists of considering a specific operator within a family of Dirac operators whose boundary conditions depend on a parameter. I will explain how to describe the spectrum of these operators using eigenvalue curves, and how properties of these curves can be used to obtain positive results in shape optimization. In particular, I will describe the connections between this problem and related shape optimization questions for the Dirichlet Laplacian, a complex version of the Robin Laplacian, and the embedding of a Hardy space into a Bergman space.
The talk is based on joint work with A. Arrizabalaga, A. Mas, and L. Vega (2023), as well as two recent works: one by J. Duran (2025), and another in collaboration with J. Duran and A. Mas (2025).