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Motivated by the study of the interrelation between functorial and algebraic quantum field theory, we point out that on any locally trivial bundle of compact groups, representations up to homotopy are enough to separate points by means of…
A fundamental result by L. Solomon in algebraic combinatorics and representation theory states that Mackey formulas for products of characters of a symmetric group, or equivalently the computation of tensor products of representations…
Inspired by the recent work by Delacretaz et. al., we rigorously derive an exact and simple method to bosonize a non-interacting fermionic system with a Fermi surface starting from a microscopic Hamiltonian. In the long-wavelength limit, we…
Let $FH$ be a Frobenius group with kernel $F$ and complement $H$, acting coprimely on the finite solvable group $G$ by automorphisms. We prove that if $C_{G}(H)$ is of Fitting length $n$ then the index of the $n$-th Fitting subgroup…
We formulate a Ginsparg-Wilson relation on a fuzzy 2-sphere for matter in the adjoint representation of the gauge group. Because of the Ginsparg-Wilson relation, an index theorem is satisfied. Our formulation is applicable to topologically…
We prove a generalization of the Fulton-Hansen connectedness theorem, where ${\mathbb P}^n$ is replaced by a normal variety on which an algebraic group acts with a dense orbit.
Unimodular gravity can be formulated so that transverse diffeomorphisms and Weyl transformations are symmetries of the theory. For this formulation of unimodular gravity, we work out the two-point and three-point $h_{\mu\nu}$ contributions…
This paper deals with the kernel-based approximation of a multivariate periodic function by interpolation at the points of an integration lattice -- a setting that, as pointed out by Zeng, Leung, Hickernell (MCQMC2004, 2006) and Zeng,…
We introduce a new pair of mutually dual bases of noncommutative symmetric functions and quasi-symmetric functions, and use it to derive generalizations of several results on the reduced incidence algebra of the lattice of noncrossing…
Factorization of the Gaussian RBF kernel is developed for free-mesh interpolation in the flat, polynomial limit corresponding to Taylor expansion and the Vandermonde basis of geometric moments. With this spectral approximation, a top-down…
We prove a very general sharp inequality of the H\"older--Young--type for functions defined on infinite dimensional Gaussian spaces. We begin by considering a family of commutative products for functions which interpolates between the…
In this paper, we use the viewpoint of Gromov-Haustorff convergence to give some new comprehension of well known theorem,it is Huber's classification theorem\cite{Huber}\cite{MS}for complete Riemannian surfaces immersed in $\mathbb{R}^n$…
Let $\Pi$ be the fundamental group of a smooth variety X over $F_p$. Given a non-Archimedean place $\lambda$ of the field of algebraic numbers which is prime to p, consider the $\lambda$-adic pro-semisimple completion of $\Pi$ as an object…
Fractal interpolation technique is an alternative to the classical interpolation methods especially when a chaotic signal is involved. The logic behind the formulation of an iterated function system for the construction of fractal…
Interpolation inequalities play an important role in the study of PDEs and their applications. There are still some interesting open questions and problems that related to integral estimates and regularity of solutions to the elliptic…
In the hyperalgebra of the $r$-th Frobenius kernel of a universal Chevalley group over a field of characteristic $p>0$, we study some subsets and the subalgebras generated by them and give some results. We are particularly interested in the…
Given an immersion of a circle in a punctured surface $\Sigma$, we give an explicit (and finite) computation of the $A_\infty$-algebra associated with this curve when viewed as an object in a (relative) Fukaya category of $\Sigma$ in terms…
Building on recent advances in studying the co-homological properties of Feynman integrals, we apply intersection theory to the computation of Fourier integrals. We discuss applications pertinent to gravitational bremsstrahlung and deep…
In this paper we consider interpolation problem connected with series by integer shifts of Gaussians. Known approaches for these problems met numerical difficulties. Due to it another method is considered based on finite-rank approximations…
Let $U$ be a smooth and connected curve over an algebraically closed field of positive characteristic, with smooth compactification $X$. We generalize classical Geometric Class Field theory to provide a classification of fppf $G$-torsors…