Related papers: Threefold Flops via Matrix Factorization
In addition to the diagonalization of a normal matrix by a unitary similarity transformation, there are two other types of diagonalization procedures that sometimes arise in quantum theory applications -- the singular value decomposition…
We consider deformations of $2\times2$ and $3\times3$ matrix linear ODEs with rational coefficients with respect to singular points of Fuchsian type which don't satisfy the well-known system of Schlesinger equations (or its natural…
In order to understand the deformations of determinants and Pfaffians resulting from deformations of matrices, we study the deformation theory of composites $f\circ F$, with isolated singularities, where $f:Y\to\C$ has Cohen-Macaulay…
We establish a correspondence between ultraviolet singularities of soft factors for multiparticle production and rapidity singularities of soft factors for multiparton scattering. This correspondence is a consequence of the conformal…
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…
We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main algorithms do not require any additional information or…
We first review the description of flag manifolds in terms of Pluecker coordinates and coherent states. Using this description, we construct fuzzy versions of the algebra of functions on these spaces in both operatorial and star product…
Motivated by an application in computational biology, we consider low-rank matrix factorization with $\{0,1\}$-constraints on one of the factors and optionally convex constraints on the second one. In addition to the non-convexity shared…
Delta lenses are functors equipped with a suitable choice of lifts, generalising the notion of split opfibration. In recent work, delta lenses were characterised as the right class of an algebraic weak factorisation system. In this paper,…
Solutions to scalar curvature equations have the property that all possible blow-up points are isolated, at least in low dimensions. This property is commonly used as the first step in the proofs of compactness. We show that this result…
In this paper we establish links between, and new results for, three problems that are not usually considered together. The first is a matrix decomposition problem that arises in areas such as statistical modeling and signal processing:…
A general theorem on factorization of matrices with polynomial entries is proven and it is used to reduce polynomial Darboux matrices to linear ones. Some new examples of linear Darboux matrices are discussed.
Polynomial factorization in conventional sense is an ill-posed problem due to its discontinuity with respect to coefficient perturbations, making it a challenge for numerical computation using empirical data. As a regularization, this paper…
We investigate the existence of complete intersection threefolds $X \subset \mathbb{P}^n$ with only isolated, ordinary multiple points and we provide some sufficient conditions for their factoriality.
We prove that the 4-dimensional Galois representations associated with a certain Calabi-Yau threefold are reducible, with 2-dimensional composition factors coming from specific modular forms of weights 2 and 4, both level 14. This was…
We study the problem of decomposition (non-commutative factorization) of linear ordinary differential operators near an irregular singular point. The solution (given in terms of the Newton diagram and the respective characteristic numbers)…
We prove two results on stacked triangulated manifolds in this paper: (a) every stacked triangulation of a connected manifold with or without boundary is obtained from a simplex or the boundary of a simplex by certain combinatorial…
We show that any nonsingular (real or complex) square matrix can be factorized into a product of at most three normal matrices, one of which is unitary, another selfadjoint with eigenvalues in the open right half-plane, and the third one is…
Using M-theory compactification, we develop a three factor separation for the scalar submanifold of N=2 seven dimensional supergravity associated with 2-cycles of the K3 surface. Concretely, we give an interplay between the three scalar…
We investigate the integer solutions of Diophantine equations related to perfect numbers. These solutions generalize the example, found by Descartes in 1638, of an odd, ``spoof'' perfect factorization $3^2\cdot 7^2\cdot 11^2\cdot 13^2\cdot…