Related papers: Freeness for multiarrangements of hyperplanes over…
Some of the multiplicity-freeness results in ``Modular Gelfand pairs and multiplicity-free representations'' are stated in overly broad generality. We provide counterexamples and partial corrections.
We examine connections between rationality of certain indefinite integrals and equilibrium of Coulomb charges in the complex plane.
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…
We define and calculate the weighted multiplicities of non Gorenstein terminal singularities on threefolds and some quotient singularities. We improve freeness conditions on threefolds.
Free noncommutative fields constitute a natural and interesting example of constrained theories with higher derivatives. The quantization methods involving constraints in the higher derivative formalism can be nicely applied to these…
This article investigates the homotopy theory of simplicial commutative algebras with a view to homological applications.
We characterize proximality of multidimensional $\mathscr{B}$-free systems in the case of number fields and lattices in $\mathbb{Z}^m$, $m\geq2$.
We define higher order infinitesimal noncommutative probability space and infinitesimal non-crossing cumulant functionals. In this framework, we generalize to higher order the notion of infinitesimal freeness, via a vanishing of mixed…
We study the Z/2-equivariant K-theory of the complement of the complexification of a real hyperplane arrangement. We compute the rational K and KO rings, and give two different combinatorial descriptions of the subring of the integral KO…
Ziegler showed that free arrangements have free restricted multiarrangements (multirestrictions). After Ziegler's work, several results concerning "reverse direction", namely characterizing freeness of an arrangement via that of…
In this article we introduce powerful tools and techniques from invariant theory to free analysis. This enables us to study free maps with involution. These maps are free noncommutative analogs of real analytic functions of several…
We study rationality problems for smooth complete intersections of two quadrics. We focus on the three-dimensional case, with a view toward understanding the invariants governing the rationality of a geometrically rational threefold over a…
We give a presentation of the motivic cohomology ring of the complement of a hyperplane arrangement considered as algebra over the motivic cohomology of the ground field.
In multipath systems, available degrees of freedom can be considered as a key performance indicator, since the channel capacity grows linearly with the available degrees of freedom. However, a fundamental question arises: given a size…
We summarize recent developments of the semiclassical description of shell effects in finite fermion systems with explicit inclusion of spin degrees of freedom, in particluar in the presence of spin-orbit interactions. We present a new…
The purpose of this paper is to show how Rees algebras can be applied in the study of singularities embedded in smooth schemes over perfect fields. In particular, we will study situations in which the multiplicity of a hypersurface is a…
We produce a one-parameter family of hyperplane arrangements that are counterexamples to the conjecture of Saito that the complexified complement of a free arrangement is $K(\pi,1)$. These arrangements are the restriction of a one-parameter…
This work is divided between two main areas: in the theory of multialgebras, we focus mostly on a new definition of what a freely generated object should be in their category, and on how this category is equivalent to another with partially…
This paper is devoted to the investigation of the property of order separability for free products of groups.
A family of polynomials linked to the set of the deltoid tangents and its associated algebraic hypersurfaces has been presented in recent years. In this paper we study some related maximising and free plane curves. We also analyse the…