Related papers: Kernel Atomicity

An algebraizable singularity is a germ of a singular holomorphic foliation which can be defined in some appropriate local chart by a differential equation with algebraic coefficients. We show that there exists at least countably many…

This Thesis presents some physically motivated criteria for the existence of particles and infra-particles in a given quantum field theory. It is based on a refined spectral theory of automorphism groups describing the energy-momentum…

We give here a simple proof of the centrality of the congruence subgroup kernel in the higher rank isotropic case.

Quantization of field-theoretic models with gauge symmetries is often obstructed by quantum anomalies. It is commonly believed that the origin of these anomalies lies in the infinite number of degrees of freedom, which requires completing…

Nowhere dense classes of graphs are very general classes of uniformly sparse graphs with several seemingly unrelated characterisations. From an algorithmic perspective, a characterisation of these classes in terms of uniform quasi-wideness,…

We show the existence of generalized clusters of a finite or even infinite number of sets, with minimal total perimeter and given total masses, in metric measure spaces homogeneous with respect to a group acting by measure preserving…

A quantum set is defined to be simply a set of nonzero finite-dimensional Hilbert spaces. Together with binary relations, essentially the quantum relations of Weaver, quantum sets form a dagger compact category. Functions between quantum…

We consider elementary particles in a quantum theory based on a Galois field. In this approach infinities cannot exist, the cosmological constant problem does not arise and one irreducible representation of the symmetry algebra necessarily…

For each prime p, we exhibit pairs of p-groups all of whose integral cohomology groups are isomorphic. The method used involves very little calculation. The groups are exhibited as kernels of homomorphisms from a compact Lie group G to…

In these lectures we present our minimality theorem by which in cohomology of a topological space appear multioperations which turn it ot Stasheff $A(\infty)$ algebra. This rich structure carries more information than just the structure of…

The Witt algebra $W_{\geq -1}$ is the Lie algebra of algebraic vector fields on a line. We investigate the two-sided ideal structure of its universal enveloping algebra, by studying the orbit homomorphisms $\Psi_n: U(W_{\geq -1})…

We prove that any complex or real analytic set or function germ is topologically equivalent to a germ defined by polynomial equations whose coefficients are algebraic numbers.

Physical theories can be characterized in terms of their state spaces and their evolutive equations. The kinematical structure and the dynamical structure of finite dimensional quantum theory are, in light of the Choi-Jamio{\l}kowski…

We prove that given a fixed finite tree $P$, almost all trees contain $P$ as a subtree. Moreover, the inclusion can be made so that it induces an embedding of the corresponding (quantum) automorphism groups, thereby providing generic…

The present work develops certain analytical tools required to construct and compute invariant kernels on the space of complex covariance matrices. The main result is the $\mathrm{L}^1$--Godement theorem, which states that any invariant…

This article presents a precise description of the interplay between the symmetries of a quantum or classical theory with spacetime interpretation, and some of its physical properties relating to causality, horizons and positive energy. Our…

At the basis of much of computational chemistry is density functional theory, as initiated by the Hohenberg-Kohn theorem. The theorem states that, when nuclei are fixed, nuclear potentials are determined by $1$-electron densities. We recast…

Many fundamental and key objects in quantum mechanics are linear mappings between particular affine/linear spaces. This structure includes basic quantum elements such as states, measurements, channels, instruments, non-signalling channels…

We examine properties of generic automorphisms of the random poset, with the goal of explicitly characterizing them. We associate to each automorphism an auxiliary first-order structure, consisting of the random poset equipped with an…

Let H be a separable infinite dimensional complex Hilbert space. We prove that every continuous 2-local automorphism of the poset (that is, partially ordered set) of all idempotents on H is an automorphism. Similar results concerning the…