Related papers: Quivers and the Adams spectral sequence
We realize the fundamental representations of quantum algebras via the supersymmetric Higgs mechanism in gauge theories with 8 supercharges on an $\Omega$-background. We test our proposal for quantum affine algebras, by probing the Higgs…
The perturbations of the Kerr metric and the miracle of their exact solutions play a critical role in the comparison of predictions of general relativity with astrophysical observations of compact massive objects. The differential equations…
We use techniques from functorial quantum field theory to provide a geometric description of the parity anomaly in fermionic systems coupled to background gauge and gravitational fields on odd-dimensional spacetimes. We give an explicit…
The paper presents a numerical analysis of the class of mathematical models of linear fractional oscillators, which is the Cauchy problem for a differential equation with derivatives of fractional orders in the sense of Gerasimov-Caputo. A…
The two dimensional set of canonical relations giving rise to minimal uncertainties previously constructed from a q-deformed oscillator algebra is further investigated. We provide a representation for this algebra in terms of a flat…
Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional $N=2$ supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra.…
In filtration 1 of the Adams spectral sequence, using secondary cohomology operations, Adams computed the differentials on the classes $h_j$, resolving the Hopf invariant one problem. In Adams filtration 2, using equivariant and chromatic…
We find a simple algebraic model for rational G-equivariant spectra, where G is the p-adic integers, via a series of Quillen equivalences. This model, along with an Adams short exact sequence, will allow us to easily perform constructions…
The cotangent complex of a map of commutative rings is a central object in deformation theory. Since the 1990s, it has been generalized to the homotopical setting of $E_\infty$-ring spectra in various ways. In this work we first establish,…
Using the spectral theorem we compute the Quantum Fourier Transform (or Vacuum Characteristic Function) $\langle \Phi, e^{itH}\Phi\rangle$ of an observable $H$ defined as a self-adjoint sum of the generators of a finite-dimensional Lie…
The question of when the derived category of a ring satisfies Brown--Adams representability is revisited via studying the transfer of pure homological dimension along definable functors: it is shown that, for any ring, the pure global…
We recall the notion of twisted parametrized spectra defined by Douglas and provide a sufficient condition for an $\infty$-category of twisted parametrized module spectra to be untwisted over an even-periodic $E_2$-ring. It is an easy…
We prove a general result that relates certain pushouts of $E_k$-algebras to relative tensors over $E_{k+1}$-algebras. Specializations include a number of established results on classifying spaces, resolutions of modules, and (co)homology…
Beyond H\"{o}lder's type, this paper mainly concerns the persistence and remaining regularity of an individual frequency-preserving KAM torus in a finitely differentiable Hamiltonian system, even allows the non-integrable part being…
q-Deformed harmonic oscillator algebra for real and root of unity values of the deformation parameter is discussed by using an extension of the number concept proposed by Gauss, namely the Q-numbers. A study of the reducibility of the Fock…
Ramification for commutative ring spectra can be detected by relative topological Hochschild homology and by topological Andr\'e-Quillen homology. In the classical algebraic context it is important to distinguish between tame and wild…
The aim of this paper is to offer an original and comprehensive spectral theoretical approach to the study of convergence to equilibrium, and in particular of the hypocoercivity phenomenon, for contraction semigroups in Hilbert spaces. Our…
We study the Hodge-to-de Rham spectral sequence for integral projective curves with local complete intersection singularities. We prove that degeneration at the E2-page is equivalent to requiring every singularity to be a quasihomogeneous…
Let $C$ be an arrangement of affine hyperplanes in a complex affine space $X$, $D$ the ring of algebraic differential operators on $X$. We define a category of quivers associated with $C$. A quiver is a collection of vector spaces, attached…
The scope of this text is to study a process that induces another proof of the Spectral Embedding Theorem: that any densely defined symmetric operator can be extended by a multiplication operator through an embedding of the Hilbert space…