Related papers: Heavy hyperplanes in multiarrangements and their f…
We prove a reformulation of the multiplicity upper bound conjecture and use that reformulation to prove it for three-dimensional simplicial complexes and homology manifolds with many vertices. We provide necessary conditions for a…
The landscape of six-dimensional supergravities is dramatically constrained by the cancellation of gauge and gravitational anomalies, but the full extent of its implications has not been uncovered. We explore the cancellation of global…
Let W be a finite complex reflection group acting on the complex vector space V and let A(W) = (A(W), V) be the associated reflection arrangement. In an earlier paper by the last two authros, we classified all inductively free reflection…
We study the change of the minimal degree of a logarithmic derivation of a hyperplane arrangement under the addition or the deletion of a hyperplane, and give a number of applications. First, we prove the existence of Tjurina maximal line…
We have studied the most general neutrino mass matrices in models with SU(2) and SU(3) horizontal symmetries. Without going into the details of the models it is possible to write down the effective operators, which predict the structure of…
A bar-and-joint framework is a finite set of points together with specified distances between selected pairs. In rigidity theory we seek to understand when the remaining pairwise distances are also fixed. If there exists a pair of points…
In this paper, we investigate weighted composition, Volterra and Integral operators on second derivative Hardy spaces. Some equivalent conditions for boundedness of the operators will be given using the boundedness on the Hardy spaces. Also…
The study of universal derivations for arbitrary multiarrangements and multiplicity functions was initiated by Abe, R\"ohrle, Stump, and Yoshinaga in 2024 which focused on arrangements arising from (well-generated) reflection groups. In…
One of the most important invariants in singularity theory is the Hodge spectrum. Calculating the Hodge spectrum is a difficult task and formulas exist for only a few cases. In this article the main result is the formula for reduced…
We present an inequality that classifies mixed multipartite systems of an arbitrary dimension with respect to separability and positivity of partial transpose properties. This inequality gives a way to experimentally classify the observed…
We define a multidimensional rearrangement, which is related to classical inequalities for functions that are monotone in each variable. We prove the main measure theoretical results of the new theory and characterize the functional…
Considering Chern-Simons like gravity theories in three dimensions as first order systems, we analyze the Hamiltonian structure of three theories Topological massive gravity, New massive gravity, and Zwei-Dreibein Gravity.We show that these…
Unitarity constraints for Yukawa couplings are considered in the Two Higgs Doublet Model type III, by using a general expansion in partial waves for fermionic scattering processes. Constraints over general Flavor Changing Neutral Currents…
We give a combinatorial criterion that implies both the non-strong relative hyperbolicity and the one-endedness of a finitely generated group. We use this to show that many important classes of groups do not admit a strong relatively…
By using the formalism of thin-shells, we construct a geometrical model of a particle in third-order Lovelock gravity. This particular theory which is valid at least in 7 dimensions, provides enough degrees of freedom and grounds towards…
We generalize the result of Kawamata concerning the strong version of Fujita's freeness conjecture for smooth 3-folds to some singular cases, namely, Gorenstein terminal singularities and quotient singularities of type 1/r(1,1,1) and of…
We discuss the discrete Z_k D-brane charges (twisted K-theory charges) in five-brane backgrounds from several different points of view. In particular, we interpret it as a result of a standard Higgs mechanism. We show that certain degrees…
In [MR21], the first two authors introduced the notion of an accurate arrangement, a particular notion of freeness. In this paper, we consider a special subclass, where the property of accuracy stems from a flag of flats in the intersection…
This article focuses on the occurrence of 3-point configurations in subsets of $\mathbb{R}^d$ of sufficient thickness. We prove that a compact set $A\subset \mathbb{R}^d$ contains a similar copy of any linear $3$-point configuration (such…
This paper begins by extending the notion of a combinatorial configuration of points and lines to a combinatorial configuration of points and planes that we refer to as configurations of order $2$. We then proceed to investigate a further…