Related papers: Fractal Weyl laws for asymptotically hyperbolic ma…
We prove that the cardinality of the torsion subgroups in homology of a closed hyperbolic manifold of any dimension can be bounded by a doubly exponential function of its diameter. It would follow from a conjecture by Bergeron and Venkatesh…
Weyl degeneracies in spectra of magnetoplasma waves enable nonreciprocal energy flow and topologically protected modes, yet conventional materials require impractical magnetic fields to operate. Developing an effective Hamiltonian framework…
Certain subsets of limit sets of geometrically finite Fuchsian groups with parabolic elements are considered. It is known that Jarn\'{\i}k limit sets determine a "weak multifractal spectrum" of the Patterson measure in this situation. This…
Given a finite graph of relatively hyperbolic groups with its fundamental group relatively hyperbolic and edge groups quasi-isometrically embedded and relatively quasiconvex in vertex groups, we prove that vertex groups are relatively…
We consider an inverse problem associated with $n$-dimensional asymptotically hyperbolic orbifolds $(n \geq 2)$ having a finite number of cusps and regular ends. By observing solutions of the Helmholtz equation at the cusp, we introduce a…
We show that each limiting semiclassical measure obtained from a sequence of eigenfunctions of the Laplacian on a compact hyperbolic surface is supported on the entire cosphere bundle. The key new ingredient for the proof is the fractal…
In this paper, we study the Selberg and Ruelle zeta functions on compact hyperbolic odd dimensional manifolds. These zeta functions are defined on one complex variable $s$ in some right half-plane of $\mathbb{C}$. We use the Selberg trace…
A variety of quantum systems exhibits Weyl points in their spectra where two bands cross in a point of three-dimensional parameters space with conical dispersion in the vicinity of the point. We consider theoretically the soft constraint…
We obtain asymptotic lower bounds for the spectral function of the Laplacian and for the remainder in local Weyl's law on manifolds. In the negatively curved case, thermodynamic formalism is applied to improve the estimates. Key ingredients…
This article is concerned with estimations from below for the remainder term in Weyl's law for the spectral counting function of certain rational (2l+1)-dimensional Heisenberg manifolds. Concentrating on the case of odd l, it continues the…
This paper continues the program that was initiated in \cite{Dav18} and continued in \cite{DSVG24}, where a high-dimensional limiting technique was developed and used to prove certain parabolic theorems from their elliptic counterparts. The…
Weyl semimetal may be thought of as a gapless topological phase protected by the chiral anomaly, where the symmetries involved in the anomaly are the $U(1)$ charge conservation and the crystal translational symmetry. The absence of a band…
We obtain bounds for the Faltings's delta function for any Riemann surface of genus greater than one. The bounds are in terms of the genus of the surface and two basic quantities coming from hyperbolic geometry: The length of the shortest…
In the first part of the paper we show Weyl type spectral asymptotic formulas for pseudodifferential operators $P_a$ of order $2a$, with type and factorization index $a\in R_+$, restricted to compact sets with boundary; this includes…
We study the asymptotic growth of the eigenvalues of the Laplace-Beltrami operator on singular Riemannian manifolds, where all geometrical invariants appearing in classical spectral asymptotics are unbounded, and the total volume can be…
We prove that all hierarchically hyperbolic spaces have finite asymptotic dimension and obtain strong bounds on these dimensions. One application of this result is to obtain the sharpest known bound on the asymptotic dimension of the…
Fractal uncertainty principle states that no function can be localized in both position and frequency near a fractal set. This article provides a review of recent developments on the fractal uncertainty principle and of their applications…
This is the first in a series of papers in which we investigate the resolvent and spectral measure on non-trapping asymptotically hyperbolic manifolds with applications to the restriction theorem, spectral multiplier results and Strichartz…
We construct Riemannian manifolds with singular continuous spectrum embedded in the absolutely continuous spectrum of the Laplacian. Our manifolds are asymptotically hyperbolic with sharp curvature bounds.
A famous result going back to Eric Kostlan states that the moduli of the eigenvalues of random normal matrices with radial potential are independent yet non identically distributed. This phenomenon is at the heart of the asymptotic analysis…