Related papers: Spectral sequences, d\'ecalage, and the Beilinson …
This note presents a discussion of the algebraic and combinatorial aspects of the theory of pure O-sequences. Various instances where pure O-sequences appear are described. Several open problems that deserve further investigation are also…
Two iterative techniques are described for decomposing a long-slit spectrum into the individual spectra of the point sources along the slit and the spectrum of the underlying background. One technique imposes the strong constraint that the…
The linear dilaton geometry in five dimensions, rediscovered recently in the continuum limit of the clockwork model, may offer a solution to the hierarchy problem which is qualitatively different from other extra-dimensional scenarios and…
Let X be a 1-connected space with free loop space LX. We introduce two spectral sequences converging towards H^*(LX;Z/p) and H^*((LX)_hT;Z/p). The E2-terms are certain non Abelian derived functors applied to H^*(X;Z/p). When H^*(X;Z/p) is a…
Resonances appearing in hadronic scattering processes are described by a two-phase model. In the one phase, scattering products are observed, whereas the other phase describes confinement. A so-called ``Resonance-Spectrum Expansion'' is…
We construct explicitly the symmetries of the isospectral deformations as twists of Lie algebras and demonstrate that they are isometries of the deformed spectral triples.
This thesis establishes the equivalence of Grayson and Friedlander-Suslin spectral sequences, that was previously only known for the respective E_2-terms. We develop the necessary techniques regarding K_0-presheaves of spectra, building on…
In this paper we give a geometric description of the general term and the differential of the Atiyah-Hirzebruch spectral sequence for $B$-bordism. This description is given in terms of bordism classes of maps from stratifolds. We illustrate…
General expository paper concerning topics in Hilbert spaces, spectral theory, and harmonic analysis. The preliminary section includes basic Banach algebra and Hilbert space theory with a digression on Riesz bases. The second and third…
This is the second paper in a series of three papers aiming to study cohomology of group theoretic Dehn fillings. In the present paper, we derive a spectral sequence for Cohen-Lyndon triples which can be thought of as a refined version of…
Quantum graphs and their experimental counterparts, microwave networks, are ideally suited to study the spectral statistics of chaotic systems. The graph spectrum is obtained from the zeros of a secular determinant derived from energy and…
The paper established sufficient conditions of predictability with degeneracy for the spectrum at $M$-periodically located isolated points on the unit circle. It is also shown that $m$-periodic subsequences of these sequences are also…
The optical spectra of fractal multilayer dielectric structures have been shown to possess spectral scalability, which has been found to be directly related to the structure's spatial (geometrical) self-similarity. Phase and amplitude…
This book offers a comprehensive introduction to spectral networks from a unified viewpoint that bridges geometry with the physics of supersymmetric gauge theories. It provides the foundational background needed to approach the frontiers of…
A dilatation structure is a concept in between a group and a differential structure. In this article we study fundamental properties of dilatation structures on metric spaces. This is a part of a series of papers which show that such a…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
The spectral problem for matrices with a block-hierarchical structure is often considered in context of the theory of complex systems. In the present article, a new class of matrices with a block-rectangular non-symmetric hierarchical…
The survey presents developments in the theory of self-similar groups leading to applications to the study of fractal sets and graphs, and their associated spectra.
The higher Leray-Serre spectral sequence associated with a tower of fibrations represents a generalization of the classical Leray-Serre spectral sequence of a fibration. In this work, we present algorithms to compute higher Leray-Serre…
The study of nuclear and subnuclear structure by means of photon scattering is outlined. Besides a brief exposition of the formalism a few illustrative examples are discussed.