Related papers: Proximality of multidimensional $\mathscr{B}$-free…

Let $(\mathscr{A},m)$ be a free multiarrangement, and let $\mathscr{E}$ be an extension of $(\mathscr{A},m)$. It is well known that if $\mathscr{A}$ is the Coxeter arrangement of type $A_2$, then a free extension of $(\mathscr{A},m)$ always…

We study multigranulation spaces of two equivalences. The lattice-theoretical properties of so-called "optimistic" and "pessimistic" multigranular approximation systems are given. We also consider the ordered sets of rough sets determined…

Let $\|\cdot\|$ be a norm on $\mathbb{R}^N$ and let $M$ be a closed $C^1$-submanifold of $\mathbb{R}^N$. Consider the pointed metric space $(M,d)$, where $d$ is the metric given by $d(x,y)=\|x-y\|$, $x,y\in M$. Then the Lipschitz-free space…

In this paper, we study the class of free multiarrangements of hyperplanes. Specifically, we investigate the relations between freeness over a field of finite characteristic and freeness over the rationals.

Let M be a B-probability space. Assume that B itself is a D-probability space; then M can be viewed as a D-probability space as well. Let X be in M. We characterize freeness of X from B with amalgamation over D in terms of a certain…

In this paper, we study the class of free hyperplane arrangements. Specifically, we investigate the relations between freeness over a field of finite characteristic and freeness over $\mathbb{Q}$.

Two quasi--biHamiltonian systems with three and four degrees of freedom are presented. These systems are shown to be separable in terms of Nijenhuis coordinates. Moreover the most general Pfaffian quasi-biHamiltonian system with an…

We define and calculate the weighted multiplicities of non Gorenstein terminal singularities on threefolds and some quotient singularities. We improve freeness conditions on threefolds.

We prove that the Hausdorff dimension of the set of badly approximable systems of m linear forms in n variables over the field of Laurent series with coefficients from a finite field is maximal. This is a analogue of Schmidt's…

We explore the structure of multipartite quantum systems which are entangled in multiple degrees of freedom. We find necessary and sufficient conditions for the characterization of tripartite systems and necessary conditions for any number…

This talk gives a review on how complex geometry and a Lagrangian formulation of 2-d conformal field theory are deeply related. In particular, how the use of the Beltrami parametrization of complex structures on a compact Riemann surface…

The paper containes a classification of consistent free string models in physical dimensions and a brief discussion of recent results concerning relations between various models.

We characterize semicircular distribution by the freeness of linear and quadratic forms in noncommutative random variables from a tracial $W^*$-probability space with relaxed moment conditions.

Let $T$ be a compact, metrisable and strongly countable-dimensional topological space. Let $\mathcal{M}^T$ be the set of all metrics $d$ on $T$ compatible with its topology, and equip $\mathcal{M}^T$ with the topology of uniform…

We consider a notion of bi-freeness for systems of non-commutative random variables with two faces, one of left variables and another of right variables. This includes bi-free convolution operations, bi-free cumulants and the bi-free…

We develop a theory of bound states in the continuum (BICs) in multipolar lattices -- periodic arrays of resonant multipoles. We predict that BICs are completely robust to changes in lattice parameters remaining pinned to specific…

We prove that for certain subsets $M \subseteq \mathbb{R}^N$, $N \geqslant 1$, the Lipschitz-free space $\mathcal{F}(M)$ has the metric approximation property (MAP), with respect to any norm on $\mathbb{R}^N$. In particular,…

We show that a free surface in $P^3$ is characterized by the maximality of the degree of its singular subscheme, in the presence of an additional tameness condition. This is similar to the characterization of free plane curves by the…

We consider the appearance of multiple scalar fields in SFT inspired non-local models with a single scalar field at late times. In this regime all the scalar fields are free. This system minimally coupled to gravity can be analyzed…

With the aim of investigating the relation between gravity and non-locality at the classical level, we study a bilocal scalar field model. Bilocality introduces new (internal) degrees of freedom that seem to reproduce gravity. We show that…