Related papers: Spectral geometry for strings and branes
A review of various aspects of superstrings in background electromagnetic fields is presented. Topics covered include the Born-Infeld action, spectrum of open strings in background gauge fields, the Schwinger mechanism, finite-temperature…
We introduce and study Brownian bridges to submanifolds. Our method involves proving a general formula for the integral over a submanifold of the minimal heat kernel on a complete Riemannian manifold. We use the formula to derive lower…
We obtain pointwise lower bounds for heat kernels of higher order differential operators with Dirichlet boundary conditions on bounded domains in $\R^N$. The bounds exhibit explicitly the nature of the spatial decay of the heat kernel close…
We describe how spectral functions of differential operators appear in the quantum field theory context. We formulate consistency conditions which should be satisfied by the operators and by the boundary conditions. We review some modern…
We study the existence and uniqueness of the heat kernel on infinite, locally finite, connected graphs. For general graphs, a uniqueness criterion, shown to be optimal, is given in terms of the maximal valence on spheres about a fixed…
We establish a new formula for the heat kernel on regular trees in terms of classical I-Bessel functions. Although the formula is explicit, and a proof is given through direct computation, we also provide a conceptual viewpoint using the…
We consider the Gurtin-Pipkin equation of the first order in time. For the kernel as a series of exponentials we obtain the structure of the spectrum of the system.
This is a mini-review of the heat kernel expansion for generalized Laplacians on various noncommutative spaces. Applications to the spectral action principle, renormalization of noncommutative theories and anomalies are also considered.
In this paper, we establish existence and uniqueness of weak solutions to general time fractional equations and give their probabilistic representations. We then derive sharp two-sided estimates for fundamental solutions of a family of time…
In this paper, we introduce heat kernel coupling (HKC) as a method of constructing multimodal spectral geometry on weighted graphs of different size without vertex-wise bijective correspondence. We show that Laplacian averaging can be…
Following is a collection of lecture notes on D-branes, which may be used by the reader as preparation for applications to modern research applications such as: the AdS/CFT and other gauge theory/geometry correspondences, Matrix Theory and…
In this paper, we firstly establish weighted heat kernel comparison theorems for the weighted heat equation on complete manifolds with radial curvatures bounded, and then by mainly using this conclusion, we can obtain two eigenvalue…
In this note we give a heat kernel lower bound in term of integral Ricci curvature, extending Cheeger-Yau's estimate.
The problem of recovering geometric properties of a domain from the trace of the heat kernel for an initial-boundary value problem arises in NMR microscopy and other applications. It is similar to the problem of ``hearing the shape of a…
Being motivated by applications to the physics of Weyl semimetals we study spectral geometry of Dirac operator with an abelian gauge field and an axial vector field. We impose chiral bag boundary conditions with variable chiral phase…
The existing research on spectral algorithms, applied within a Reproducing Kernel Hilbert Space (RKHS), has primarily focused on general kernel functions, often neglecting the inherent structure of the input feature space. Our paper…
The aim of this article is to establish two-sided Gaussian bounds for the heat kernels on the unit ball and simplex in $\mathbb{R}^n$, and in particular on the interval, generated by classical differential operators whose eigenfunctions are…
We study boundary values of holomorphic functions in translation-invariant distribution spaces of type $\mathcal{D}'_{E'_{\ast}}$. New edge of the wedge theorems are obtained. The results are then applied to represent…
Spectral kernel methods are techniques for transforming data into a coordinate system that efficiently reveals the geometric structure - in particular, the "connectivity" - of the data. These methods depend on certain tuning parameters. We…
Heat diffusion has been widely used in brain imaging for surface fairing, mesh regularization and cortical data smoothing. Motivated by diffusion wavelets and convolutional neural networks on graphs, we present a new fast and accurate…