14h:00-16h:00 | (02/06/2023)
Prof. Rodrigo Matos - Professor do Departamento de Matemática | PUC-Rio
The structure of the dispersion relation is one of the central aspects to the study of periodic Schroedinger operators.
Besides the intrinsic interest from the viewpoint of several complex variables and algebraic geometry, the dispersion relation also carries relevant information
for the spectral theory of periodic media. In particular, for the structure of spectral boundaries, isospectrality, and existence of eigenvalues for locally perturbed operators.
I will discuss some of these connections as well as recent irreducibility theorems for the Bloch and Fermi varieties,
focusing on two joint works with Jake Fillman and Wencai Liu (arXiv:2107.06447 & J. Funct. Anal. 2022, arXiv 2305.06471).
These recent papers cover a wide class of lattice geometries in arbitrary dimension and verify the discrete version of certain conjectures of Kuchment for various discrete models.