Related papers: Indefinite structure of the Bergman kernel on the …
In this paper, we survey recent works on the structure of the mapping class groups of surfaces mainly from the point of view of topology. We then discuss several possible directions for future research. These include the relation between…
This article presents a technique for analytic interpolation over the exterior of a unit disk using complex poles in the interior--as well as corresponding techniques for the exterior of a real unit disk and for the interior of a real and…
The asymptotic analysis of Bergman kernels with respect to exponentially varying measures near emergent interfaces has attracted recent attention. Such interfaces typically occur when the associated limiting Bergman density function…
Given a topological space $X$, a thickening kernel is a monoidal presheaf on $(\mathbb{R}_{\geq0},+)$ with values in the monoidal category of derived kernels on $X$. A bi-thickening kernel is defined on $(\mathbb{R},+)$. To such a…
We introduce a theory of local kernels, which generalize the kernels used in the standard diffusion maps construction of nonparametric modeling. We prove that evaluating a local kernel on a data set gives a discrete representation of the…
We consider the unitary group $\U$ of complex, separable, infinite-dimensional Hilbert space as a discrete group. It is proved that, whenever $\U$ acts by isometries on a metric space, every orbit is bounded. Equivalently, $\U$ is not the…
The skyrmion, which is characterised by a topological integer, is a structure that is topologically stable against local disturbances. The huge potential of skyrmions for use in magnetic storage systems has drawn considerable research…
The goal of this note is to explore the Bergman projection on forms. In particular, we show that some of most basic facts used to construct the Bergman kernel on functions, such as pointwise evaluation in…
A construction is given of Markov partitions for some rational maps, which persist over regions of parameter space, not confined to single hyperbolic components. The set on which the Markov partition exists, and its boundary, are analysed.
We study the kernel/metric correspondence pointed out in our previous work in a dissipative system which is accompanying fractional Brownian motion. We also give some comments on information causality.
This article investigates structural connections between unrefinable partitions into distinct parts and numerical semigroups. By analysing the hooksets of Young diagrams associated with numerical sets, new criteria for recognising…
We analyse properties of contact networks formed in packings of soft frictionless disks near the unjamming transition. We construct polygonal tilings and triangulations of the contact network that partitions space into convex regions which…
This paper investigates the failure of certain metric measure spaces to be infinitesimally Hilbertian or quasi-Riemannian manifolds, by constructing examples arising from a manifold $M$ endowed with a Riemannian metric $g$ that is possibly…
We obtain the octonionic Bergman kernel for half space in the octonionic analysis setting by two different methods. As a consequence, we unify the kernel forms in both complex analysis and hyper-complex analysis.
We present a generalization of the notion of an algebra norm relevant to real finite-dimensional unital associative algebras. Among other things, this leads to a novel set of algebra isomorphism invariants, some of which are computationally…
This work deals with relations between a bounded cohomological invariant and the geometry of Hermitian symmetric spaces of noncompact type. The invariant, obtained from the K\"ahler class, is used to define and characterize a special class…
We present an elementary proof for an approximate expression of the Bergman kernel on homogeneous spaces, and products of them. The error term is exponentially small with respect to the inverse semiclassical parameter.
Hermitian bundle gerbes with connection are geometric objects for which a notion of surface holonomy can be defined for closed oriented surfaces. We systematically introduce bundle gerbes by closing the pre-stack of trivial bundle gerbes…
A long-standing question is what invariant sets can be shared by two maps acting on the same space. A similar question stands for invariant measures. A particular interesting case are expanding Markov maps of the circle. If the two involved…
The purpose of this paper is to announce some new results on the structure of the higher order Euler-Lagrange mapping of the multiple-integral variational calculus on fibered manifolds,namely a description of its kernel and its image,and an…