Related papers: Spectral theory and the Eigenvariety machine
This script is based on the notes the author prepared to give a set of six lectures at the Les Houches School "Integrability in Atomic and Condensed Matter Physics" in the summer of 2018. The school had its focus on the application of…
Sparsity-based representations have recently led to notable results in various visual recognition tasks. In a separate line of research, Riemannian manifolds have been shown useful for dealing with features and models that do not lie in…
This thesis is concerned with the application of operadic methods, particularly modular operads, to questions arising in the study of moduli spaces of surfaces as well as applications to the study of homotopy algebras and new constructions…
This article is devoted the semiclassical spectral analysis of the Neumann magnetic Laplacian on a smooth bounded domain in three dimensions. Under a generic assumption on the variable magnetic field (involving a localization of the…
Consider the empirical autocovariance matrix at a given non-zero time lag based on observations from a multivariate complex Gaussian stationary time series. The spectral analysis of these autocovariance matrices can be useful in certain…
We offer a spectral analysis for a class of transfer operators. These transfer operators arise for a wide range of stochastic processes, ranging from random walks on infinite graphs to the processes that govern signals and recursive wavelet…
Recent advances in computer vision and machine learning suggest that a wide range of problems can be addressed more appropriately by considering non-Euclidean geometry. In this paper we explore sparse dictionary learning over the space of…
A common challenge faced in quantum physics is finding the extremal eigenvalues and eigenvectors of a Hamiltonian matrix in a vector space so large that linear algebra operations on general vectors are not possible. There are numerous…
Foundations of the theory of vertex algebras are extended to the non-Archimedean setting.
Equivariant machine learning methods have shown wide success at 3D learning applications in recent years. These models explicitly build in the reflection, translation and rotation symmetries of Euclidean space and have facilitated large…
In this paper we show variant of the spectral theorem using an algebraic Jordan-Schwinger map. The advantage of this approach is that we don't have restriction of normality on the class of operators we consider. On the other side, we have…
Representations in the auditory cortex might be based on mechanisms similar to the visual ventral stream; modules for building invariance to transformations and multiple layers for compositionality and selectivity. In this paper we propose…
These lecture notes are based on an introductory course given by the author at the summer school "Noncommutative Algebraic Geometry" at MSRI in June 2012. The emphasis throughout is on examples to illustrate the many different facets of…
The Euclidean distance degree of an algebraic variety is a well-studied topic in applied algebra and geometry. It has direct applications in geometric modeling, computer vision, and statistics. We use non-proper Morse theory to give a…
Non-Hermitian (NH) systems exhibit intricate spectral topology arising from complex-valued eigenenergies, with positive/negative imaginary parts representing gain/loss. Unlike the orthogonal eigenstates of Hermitian systems, NH systems…
The first-order model theory of modules has been studied for decades. More recently, the model theoretic study of nonelementary classes of modules--especially Abstract Elementary Classes of modules--has produced interesting results. This…
Our purpose is to make a contribution to the foundation of the theory of formal scheme. We are interested particularly in non-Noetherian or non-adic formal schemes, which have been little studied. We redefine the formal scheme as a…
In this paper spectral theorems for not necessarily continuous normal and self-adjoint random operators on a complex separable Hilbert space are proved.
In this article we present an elementary introduction to the theory of minimal surfaces in Euclidean spaces $\mathbb R^n$ for $n\ge 3$ by using only elementary calculus of functions of several variables at the level of a typical second-year…
The goal of these lectures is to explain speaker's results on uniqueness properties of spherical varieties. By a uniqueness property we mean the following. Consider some special class of spherical varieties. Define some combinatorial…