Related papers: The spectral localizer for even index pairings
The spectra of signed matrices have played a fundamental role in social sciences, graph theory, and control theory. In this work, we investigate the computational problems of identifying symmetric signings of matrices with natural spectral…
In this paper, we explore spectral measures whose square integrable spaces admit a family of exponential functions as an orthonormal basis.Our approach involves utilizing the integral periodic zeros set of Fourier transform to characterize…
Colocalization is a right adjoint to the inclusion of a subcategory. Given a ring-spectrum R, one would like a spectral sequence which connects a given colocalization in the derived category of R-modules and an appropriate colocalization in…
Equivariant complex $K$-theory and the equivariant sphere spectrum are two of the most fundamental equivariant spectra. For an odd $p$-group, we calculate the zeroth homotopy Green functor of the localization of the equivariant sphere…
A linear mapping upon real n-dimensional space, where the dimension n is odd, has a real eigenvalue-eigenvector pair. The corresponding statement for complex vector spaces holds true for any dimension n, but should be easy to demonstrate…
We construct functors sending torus-equivariant quasi-coherent sheaves on toric schemes over the sphere spectrum to constructible sheaves of spectra on real vector spaces. This provides a spectral lift of the toric homolgoical mirror…
We perform a computational spectral analysis of different isospectrally patterned lattices (IPL). Having been introduced very recently, the lattice Hamiltonian of IPL consist of coupled cells which possess all the same set of eigenvalues.…
We present a simple proof of a precise version of the localization theorem in equivariant cohomology. As an application, we describe the cohomology algebra of any compact symplectic variety with a multiplicity-free action of a compact Lie…
We prove the formula for the traces of certain class of operators in bosonic and fermionic Fock spaces. Vertex operators belong to this class. Traces of vertex operators can be used for calculation of correlation functions and formfactors…
Let $X$ be a rational homogeneous space and let $QH^*(X)_{loc}^\times$ be the group of invertible elements in the small quantum cohomology ring of $X$ localised in the quantum parameters. We generalise results of arXiv:math/0609796 and…
The bicategory of parameterized spectra has a remarkably rich structure. In particular, it is possible to take traces in this bicategory, which give classical invariants that count fixed points. We can also take equivariant traces, which…
A new method to enclose the pseudospectrum via the numerical range of the inverse of a matrix or linear operator is presented. The method is applied to finite-dimensional discretizations of an operator on an infinite-dimensional Hilbert…
We describe spectra of associative (not necessarily unital and not necessarily countable-dimensional) locally matrix algebras. We determine all possible spectra of locally matrix algebras and give a new proof of Dixmier-Baranov Theorem. As…
For the algebra $\mI_1= K<x, \frac{d}{dx}, \int>$ of polynomial integro-differential operators over a field $K$ of characteristic zero, a classification of simple modules is given. It is proved that $\mI_1$ is a left and right coherent…
We provide a characterization of homogeneous spaces under a reductive group scheme such that the geometric stabilizers are maximal tori. The quasi-split case over a semilocal base is of special interest and permits to answer a question…
Infinite-dimensional Lie algebras are introduced, which are only partially graded, and are specified by indices lying on cyclotomic rings. They may be thought of as generalizations of the Onsager algebra, but unlike it, or its sl(n)…
Almost flat finitely generated projective Hilbert C*-module bundles were successfully used by Hanke and Schick to prove special cases of the Strong Novikov Conjecture. Dadarlat later showed that it is possible to calculate the index of a…
There are well-known constructions relating ring epimorphisms and tilting modules. The new notion of silting module provides a wider framework for studying this interplay. To every partial silting module we associate a ring epimorphism…
Link homotopy has been an active area of research for knot theorists since its introduction by Milnor in the 1950s. We introduce a new equivalence relation on spatial graphs called component homotopy, which reduces to link homotopy in the…
It is shown that a transparent birefringent element whose eigenstates are a pair of elliptical polarizations with principalaxes along the x and y axes, sandwiched between a pair of orthogonal halfwave plates with principal axes along…