Related papers: Some geometric and spectral aspects of restriction…
Motivated by research on contraction analysis and incremental stability/stabilizability the study of 'differential properties' has attracted increasing attention lately. Previously lifts of functions and vector fields to the tangent bundle…
Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative…
We consider the generalized spectral estimation problem in infinite dimensional spaces. We solve this problem using the boundary control approach to inverse theory and provide an application to the initial boundary value problem for a…
When a numerical simulation has to handle a physics problem with a wide range of time-dependent length scales, dynamically adaptive discretizations can be the method of choice. We present a major upgrade to the numerical relativity code…
We derive a new lower bound for the bandwidth of a graph that is based on a new lower bound for the minimum cut problem. Our new semidefinite programming relaxation of the minimum cut problem is obtained by strengthening the known…
We first provide an overview of several results dealing with the genus of a division algebra and highlight the role of ramification in its analysis. We then give a survey of recent developments on the genus problem for simple algebraic…
In these lectures I will present an introduction to the results that have been recently obtained in constraint optimization of random problems using statistical mechanics techniques. After presenting the general results, in order to…
We study the dependence of the quantum graph Hamiltonian, its resolvent, and its spectrum on the vertex conditions and graph edge lengths. In particular, several results on the interlacing (bracketing) of the spectra of graphs with…
Statistical modeling can involve a tension between assumptions and statistical identification. The law of the observable data may not uniquely determine the value of a target parameter without invoking a key assumption, and, while…
The restriction and Kakeya problems in Euclidean space have received much attention in the last few decades, and are related to many problems in harmonic analysis, PDE, and number theory. In this paper we initiate the study of these…
The paper investigates solutions of the fractional hyperbolic diffusion equation in its most general form with two fractional derivatives of distinct orders. The solutions are given as spatial-temporal homogeneous and isotropic random…
In this paper we revisit a discrete spectral problem which was proposed by Ragnisco and Tu in 1989, as a second discretization of the ZS-AKNS spectral problem. We show that the spectral problem corresponds to a bidirectional discretization…
We consider the problem of finding a Hamiltonian path or cycle with precedence constraints in the form of a partial order on the vertex set. We study the complexity for graph width parameters for which the ordinary problems…
The concept of boundary plays an important role in several branches of general relativity, e.g., the variational principle for the Einstein equations, the event horizon and the apparent horizon of black holes, the formation of trapped…
The local properties problem of Erd\H{o}s and Shelah generalizes many Ramsey problems and some distinct distances problems. In this work, we derive a variety of new bounds for the local properties problem and its variants. We do this by…
This is a textbook on arithmetic geometry with special regard to unramified Brauer groups of algebraic varieties. The topics include Galois cohomology, Brauer groups, obstructions to stable rationality, arithmetic and geometry of quadrics,…
Algebraic statistics is concerned with the study of probabilistic models and techniques for statistical inference using methods from algebra and geometry. This article presents a list of open mathematical problems in this emerging field,…
We establish connections between different approaches to inverse spectral problems: the classical Gelfand--Levitan theory, the Krein method, the Simon theory, the approach proposed by Remling and the Boundary Control method. We show that…
Noncommutative spectral geometry offers a purely geometric explanation for the standard model of strong and electroweak interactions, including a geometric explanation for the origin of the Higgs field. Within this framework, the…
The variation of spectral subspaces for linear self-adjoint operators under an additive bounded perturbation is considered. The objective is to estimate the norm of the difference of two spectral projections associated with isolated parts…