Periodic operators on universal covering trees are (in a precise sense) the non-commutative analog of periodic operators on lattices of the Euclidean space. Many results (derived via Floquet theory) that hold true for lattices turn out to have a natural valid analog for periodic operators on universal covering trees (although no unifying theory has yet been developed in the latter setting).

In this talk I will discuss these parallels and announce a recent generalization of the Thouless formula (from the theory of tridiagonal Schrodinger operators) that enables the study of periodic operators on universal covering trees. This is joint work with Jess Banks, Jonathan Breuer, Eyal Seelig and Barry Simon.

Bio: Jorge Garza-Vargas is a Mexican mathematician. He earned his Ph.D. from the Mathematics Department at UC Berkeley in December of 2022, under the supervision of Nikhil Srivastava and Dan-Virgil Voiculescu. He is currently a postdoc in the department of Computational and Mathematical Sciences at Caltech. He works on spectral problems in the context of algorithms, random matrices, analytic theory of polynomials, and functional analysis.