Dispersion relations and Fermi surfaces for periodic operators of mathematical physics are
some of the most common and important notions in condensed matter physics, in particular …

The oscillation of a Laplacian eigenfunction gives a great deal of information about the
manifold on which it is defined. This oscillation can be encoded in the nodal deficiency, an …

For periodic graph operators, we establish criteria to determine the overlaps of spectral band
functions based on Bloch varieties. One criterion states that for a large family of periodic …

We study the spectra of operators on periodic graphs using methods from combinatorial
algebraic geometry. Our main result is a bound on the number of complex critical points of …

We consider a compact perturbation H0 DSCK 0 K0 of a self-adjoint operator S with an
eigenvalue ı below its essential spectrum and the corresponding eigenfunction f. The …

In this paper, we develop certain aspects of perturbation theory for self‐adjoint operators
subject to small variations of their domains. We use the abstract theory of boundary triplets to …

We consider discrete Schr\" odinger operators with periodic potentials on periodic graphs.
Their spectra consist of a finite number of bands. By" rolling up" a periodic graph along some …

In this paper we develop a systematic calculus for the Duistermaat index, a symplectic
invariant defined for triples of Lagrangian subspaces. Introduced nearly half a century ago …

Unique continuation principles are fundamental properties of elliptic partial differential
equations, giving conditions that guarantee that the solution to an elliptic equation must be …

The oscillation of a Laplacian eigenfunction gives a great deal of information about the
manifold on which it is defined. This oscillation can be encoded in the nodal deficiency, an …