相关论文: Conjectures on spectral numbers for upper triangul…

Operadic tangent cohomology generalizes the existing cohomology theories of Chevalley--Eilenberg, Hochschild, and Harrison to address the deformation theory of general types of algebras through gadgets known as deformation complexes. The…

We propose a Lie-theoretic definition of the tt*-Toda equations for any complex simple Lie algebra $\mathfrak{g}$, based on the concept of topological-antitopological fusion which was introduced by Cecotti and Vafa. Our main result concerns…

A general theory of matrix-spherical functions for dual Hopf algebras and right coideal subalgebras is developed. We establish their existence and define their orthogonality relations. When specialized to Kolb and Letzter's quantum…

The concept of a fully interlacing matrix of formal power series with real coefficients is introduced. This concept extends and strengthens that of an interlacing sequence of real-rooted polynomials with nonnegative coefficients, in the…

Vertex algebras that arise from four-dimensional, $\mathcal{N}=2$ superconformal field theories inherit a collection of novel structural properties from their four-dimensional ancestors. Crucially, when the parent SCFT is unitary, the…

Schubert calculus has been in the intersection of several fast developing areas of mathematics for a long time. Originally invented as the description of the cohomology of homogeneous spaces it has to be redesigned when applied to other…

Spectral functions of symmetric matrices -- those depending on matrices only through their eigenvalues -- appear often in optimization. A cornerstone variational analytic tool for studying such functions is a formula relating their…

A formalism for study of spectral correlations in non-Gaussian, unitary invariant ensembles of large random matrices with strong level confinement is reviewed. It is based on the Shohat method in the theory of orthogonal polynomials. The…

We investigate the properties of sparse matrix ensembles with particular regard for the spectral ergodicity hypothesis, which claims the identity of ensemble and spectral averages of spectral correlators. An apparent violation of the…

We propose a conjectural semiorthogonal decomposition for the derived category of the moduli space of stable rank 2 bundles with fixed determinant of odd degree, independently formulated by Narasimhan. We discuss some evidence for, and…

The fact that each finite-dimensional algebra over a field is isomorphic to the centralizer of two matrices, has suggested to investigate representation theoretical problems of finite-dimensional algebras through centralizer algebras of…

Pseudospectral analysis serves as a powerful tool in matrix computation and the study of both linear and nonlinear dynamical systems. Among various numerical strategies, random sampling, especially in the form of rank-$1$ perturbations,…

Let $A$ be a square matrix and let $\Omega$ be an open set in the plane containing the spectrum of $A$. We consider the problem of maximizing the operator norm $\|f(A)\|$ amongst all holomorphic functions $f$ from $\Omega$ into the closed…

For convex and sequential effect algebras, we study spectrality in the sense of Foulis. We show that under additional conditions (strong archimedeanity, closedness in norm and a certain monotonicity property of the sequential product), such…

A classical theorem of Wendroff shows that one may reconstructs a sequence of orthogonal polynomials on the real line from two non-constant polynomials of consecutive degrees whose zeros strictly interlace on the real line. In this note we…

Classical spectral theory gives a complete description of a single normal operator, but it fails for noncommuting operators, where no canonical joint spectrum or simultaneous diagonalization exists. Existing approaches provide only partial…

In Part I (arXiv:1209.2045) we computed the Stokes data, though not the "connection matrix", for the smooth solutions of the tt*-Toda equations whose existence we established by p.d.e. methods. Here we give an alternative proof of the…

We use F. Ferrari's methods relating matrix models to Calabi-Yau spaces in order to explain much of Intriligator and Wecht's ADE classification of $\N=1$ superconformal theories which arise as RG fixed points of $\N = 1$ SQCD theories with…

Isolated hypersurface singularities come equipped with distinguished bases of their Milnor lattices and with upper triangular integral matrices, which are called here distinguished matrices. These matrices form an orbit of a braid group and…

This paper provides a complete proof of Simon-Lukic conjecture for orthogonal polynomials on the unit circle. For a probability measure $d\mu = w(\theta) \frac{d\theta}{2\pi} + d\mu_s$ with Verblunsky coefficients…