Related papers: Relatively spectral morphisms and applications to …
This is a survey article with the goal to advertise spectrum valued versions of $K$- and $KK$- theory for $C^{*}$-algebras via a (stable and symmetric monoidal) $\infty$-categorical enhancement of Kasparov's classical $KK$-theory. The main…
We construct a motivic spectral sequence for the relative homotopy invariant K-theory of a closed immersion of schemes $D \subset X$. The $E_2$-terms of this spectral sequence are the cdh-hypercohomology of a complex of equi-dimensional…
We consider the problem of determining the complexity of the uniform homeomorphism relation between separable Banach spaces in the Borel reducibility hierarchy of analytic equivalence relations. We prove that the complete $K_{\sigma}$…
A map between string junctions in the affine 7-brane backgrounds and vector bundles on del Pezzo surfaces is constructed using mirror symmetry. It is shown that the lattice of string junctions with support on an affine 7-brane configuration…
We consider a non-relativistic quantum particle interacting with a singular potential supported by two parallel straight lines in the plane. We locate the essential spectrum under the hypothesis that the interaction asymptotically…
We study some natural generalizations of the spectral spaces in the contexts of commutative rings and distributive lattices. We obtain a topological characterization for the spectra of commutative (not necessarily unitary) rings and we find…
We prove a Corona type theorem with bounds for the Sarason algebra $H^\infty+C$ and determine its spectral characteristics. We also determine the Bass, the dense, and the topological stable ranks of $H^\infty+C$.
For appropriate parameters $k,p,q$, we introduce and systematically study the class of $(k,p,q)$-differential subalgebras. This is a vast class of Banach $^*$-algebras defined by their relation with their $C^*$-envelopes. Some examples are…
We introduce a family of Banach spaces of measures, each containing the set of measures with density of bounded variation. These spaces are suitable for the study of weighted transfer operators of piecewise-smooth maps of the interval where…
We define higher semiadditive algebraic K-theory, a variant of algebraic K-theory that takes into account higher semiadditive structure, as enjoyed for example by the $K(n)$- and $T(n)$-local categories. We prove that it satisfies a form of…
We introduce the notion of a conformal de Rham complex of a Riemannian manifold. This is a graded differential Banach algebra and it is invariant under quasiconformal maps, in particular the associated cohomology is a new quasiconformal…
We summarize recent results initiating spectral analysis on pseudo-Riemannian locally symmetric spaces $\Gamma \backslash G/H$, beyond the classical setting where $H$ is compact (e.g. theory of automorphic forms for arithmetic $\Gamma$) or…
The unification of general relativity with quantum theory will also require a coming together of the two quite different mathematical languages of general relativity and quantum theory, i.e., of differential geometry and functional analysis…
The explicit solution to the spectral problem of quantum graphs found recently in \cite{Anima}, is used to produce the exact periodic orbit theory description for the probability distributions of spectral statistics, including the…
We consider the SU_q (N) invariant spin chain with diagonal and non-diagonal integrable boundary terms. The algebraic study of spin chains with different types of boundary terms is used to motivate a set of spectral equivalences between…
We develop a sheaf cohomology theory of algebraic varieties over an algebraically closed non-trivially valued non-archimedean field $K$ based on Hrushovski-Loeser's stable completion. In parallel, we develop a sheaf cohomology of definable…
Our main result is the proof of an inequality between the spectral numbers of a Lagrangian and the spectral numbers of its reductions, in the opposite direction to the classical inequality (see e.g [Vit92]). This has applications to the…
We extend the notion of an almost flat bundle over a closed Riemannian manifold to bundles over simplicial complexes, and prove that up to a constant factor, this notion is invariant under pullback via maps which induce isomorphisms on…
We study twisted derived equivalences for schemes in the setting of spectral algebraic geometry. To this end, we introduce the notion of a twisted equivalence and show that a twisted equivalence for perfect spectral algebraic stacks…
The quantum lens spaces form a natural and well-studied class of noncommutative spaces which can be subjected to classification using algebraic invariants by drawing on the fully developed classification theory of unital graph…