Related papers: Laplacian operators and Radon transforms on Grassm…

Denote the Laplacian of a graph $G$ by $L(G)$ and its second smallest Laplacian eigenvalue by $\lambda_2(G)$. If $G$ is a graph on $n\ge 2$ vertices, then it is shown that the second smallest eigenvalue of $L(G) + \frac{1}{n}…

Let $G$ be a locally compact abelian group with a Haar measure, and $Y$ be a measure space. Suppose that $H$ is a reproducing kernel Hilbert space of functions on $G\times Y$, such that $H$ is naturally embedded into $L^2(G\times Y)$ and is…

We study algebraic isomonodromic deformations of flat logarithmic connections on the Riemann sphere with $n\geq 4$ poles, for arbitrary rank. We introduce a natural property of algebraizability for the germ of universal deformation of such…

Let $X$ be a compact Riemann surface of genus $g\geq 2$ equipped with flat conical metric $|\Omega|$, where $\Omega$ be a holomorphic quadratic differential on $X$ with $4g-4$ simple zeroes. Let $K$ be the canonical line bundle on $X$.…

We review the properties of eigenvectors for the graph Laplacian matrix, aiming at predicting a specific eigenvalue/vector from the geometry of the graph. After considering classical graphs for which the spectrum is known, we focus on…

This paper constructs weight-shifting integral operators for Maass forms on the full modular group SL(2,Z). Under the weight parity condition t = k (mod 2), the operator utilizes an automorphic kernel constructed via Poincare series from a…

In this paper we study the Grassmannian of submodules of a given dimension inside a finitely generated projective module $P$ for a finite dimensional algebra $\Lambda$ over an algebraically closed field. The orbit of such a submodule $C$…

We propose an algebraic framework for generalized graph Laplacians which unifies the study of resistor networks, the critical group, and the eigenvalues of the Laplacian and adjacency matrices. Given a graph with boundary $G$ together with…

Bayesian optimization is a data-efficient technique which can be used for control parameter tuning, parametric policy adaptation, and structure design in robotics. Many of these problems require optimization of functions defined on…

We obtain a combinatorial expression for the coefficients of the boundary map of real isotropic and odd orthogonal Grassmannians providing a natural generalization of the formulas already obtained for Lagrangian and maximal isotropic…

Let $G$ be a finite pseudoreflection group and $\Omega\subseteq \mathbb C^d$ be a bounded domain which is a $G$-space. We establish identities involving Toeplitz operators on the weighted Bergman spaces of $\Omega$ and $\Omega/G$ using…

The Clebsch--Gordan coefficients of $U(\mathfrak{sl}_2)$ are expressible in terms of Hahn polynomials. The phenomenon can be explained by an algebra homomorphism $\natural$ from the universal Hahn algebra $\mathcal H$ into…

We work with $N-$dimensional compact real hyperbolic space $X_{\Gamma}$ with universal covering $M$ and fundamental group $\Gamma$. Therefore, $M$ is the symmetric space $G/K$, where $G=SO_1(N,1)$ and $K=SO(N)$ is a maximal compact subgroup…

Let G be a complex semisimple group and U its maximal unipotent subgroup. We study the algebra D(G/U) of algebraic differential operators on G/U and also its quasi-classical counterpart: the algebra of regular functions on the cotangent…

We study singular integral operators induced by $3$-dimensional Calder\'on-Zygmund kernels in the Heisenberg group. We show that if such an operator is $L^{2}$ bounded on vertical planes, with uniform constants, then it is also $L^{2}$…

We solve the following problem: to describe in geometric terms all differential operators of the second order with a given principal symbol. Initially the operators act on scalar functions. Operator pencils acting on densities of arbitrary…

For $G=\mathrm{SL}_2$ or $\mathrm{GL}_2$, we present explicit formulas for the nonabelian Fourier kernels on $G$, as conjectured by A. Braverman and D. Kazhdan. Additionally, we furnish explicit formulas for the orbital Hankel transform on…

We study infinite weighted graphs with view to \textquotedblleft limits at infinity,\textquotedblright or boundaries at infinity. Examples of such weighted graphs arise in infinite (in practice, that means \textquotedblleft…

For a quadratic extension $\mathbb{E}/\mathbb{F}$ of non-archimedean local fields we construct explicit holomorphic families of intertwining operators between principal series representations of $\operatorname{PGL}(2,\mathbb{E})$ and…

Lax operator algebras for the root system $G_2$, and arbitrary finite genus Riemann surfaces and Tyurin data on them are constructed.