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The aim of this note is to extend the notion of commutativity of vector fields to the category of singular foliations, using Nambu structures, i.e. integrable multi-vector fields. We will show some ba...
We start with a Riemann-Hilbert Problems (RHP) with canonical normalization whose sewing functions depends on several additional variables. Using Zakharov-Shabat theorem we are able to construct a fam...
In this note, one discusses about some varieties which are constructed analogously to the isospectral commuting varieties. These varieties are subvarieties of varieties having very simple desingulariz...
Abstract: The behavior of fermionic systems depends on the geometry of the system and the symmetry class of the Hamiltonian and observables. Almost commuting matrices arise from band-projected positio...
Abstract: In this paper we give enough conditions when the operator of the fourth order included in a commutative ring of ordinary differential operators of rank 2 is formally self-adjoint. In the cas...
Abstract: We show how to map the states of an ergodic Markov chain to Euclidean space so that the squared distance between states is the expected commuting time. We find a minimax characterization of ...
Abstract: We give a natural generalization of the classification of commutative rings of ordinary differential operators, given in works of Krichever, Mumford, Mulase, and determine commutative rings ...
In this note we prove that there exist at least two examples of three commuting, unital, completely positive maps that have no dilation on a type I factor, and no minimal dilation on any von Neumann a...
We calculate the diameters of commuting graphs of matrices over the bi-nary Boolean semiring, the tropical semiring and an arbitrary nonentire commutative semiring. We also find the lower bound for th...
We show that a pair of almost commuting self-adjoint, symmetric ma-trices are close to commuting self-adjoint, symmetric matrices (in a uni-form way).
We introduce the notion of joint torsion for several commuting operators satisfying a Fredholm condition. This new secondary invariant takes values in the group of invertibles of a field. It is const...
Type-I matrices were introduced recently as finite dimensional prototypes of quantum integrable systems. These matrices are linearly dependent on an "interaction" type parameter, and possess interesti...
We consider quantum key distribution in the device-independent scenario, i.e., where the legitimate parties do not know (or trust) the exact specification of their apparatus. We show how secure key ...
The aim of this paper is to describe the irregular locus of the commuting variety of a reductive symmetric Lie algebra. More precisely, we want to enlighten a remark of Popov. In [Po], the irregular l...
In this article, we provide two different ways of producing recursive formulas for the Rayleigh functions of eigenvalues of the one-dimensional Laplacian with non-local boundary conditions, which comm...

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