Related papers: Degree-d-invariant laminations

A topological invariant of a polynomial map $p:X\to B$ from a complex surface containing a curve $C\subset X$ to a one-dimensional base is given by a rational second homology class in the compactification of the moduli space of genus $g$…

For a dominant rational self-map on a smooth projective variety defined over a number field, Kawaguchi and Silverman conjectured that the (first) dynamical degree is equal to the arithmetic degree at a rational point whose forward orbit is…

Let ${\cal D}^k$ be the space of $k$-th order linear differential operators on ${\bf R}$: $A=a_k(x)\frac{d^k}{dx^k}+\cdots+a_0(x)$. We study a natural 1-parameter family of $\Diff(\bf R)$- (and $\Vect(\bf R)$)-modules on ${\cal D}^k$. (To…

Dynamical degrees and spectra can serve to distinguish birational automorphism groups of varieties in quantitative, as opposed to only qualitative, ways. We introduce and discuss some properties of those degrees and the Cremona degrees,…

The entanglement characteristics of two qubits are encoded in the invariants of the adjoint action of SU(2) x SU(2) group on the space of density matrices defined as the space of positive semi-definite Hermitian matrices. The corresponding…

We study the entanglement entropy of random partitions in one- and two-dimensional critical fermionic systems. In an infinite system we consider a finite, connected (hypercubic) domain of linear extent $L$, the points of which with…

Let $k$ be a field and let $V$ be a $k$-vector space of dimension $d$. Let $G \subseteq GL(V)$ be a finite group. Let $r = \dim_k (V^*)^G$. Assume $r \geq 1$. Let $R = k[V]^G$ be the ring of invariants of $G$. Let $H_R(n) =…

We prove the so-called master relation in the tautological ring of the moduli space of curves that implies polynomial properties of the Dubrovin-Zhang hierarchies associated to different versions of cohomological field theories as well as…

We study Voronoi percolation on a large class of $d$-dimensional Riemannian manifolds, which includes the hyperbolic spaces $\mathbb{H}^d$, $d\geq 2$. We prove that as the intensity $\lambda$ of the underlying Poisson point process tends to…

We establish Monod's isomorphism conjecture in degree-three bounded cohomology for every complex simple Lie group of classical type. Our main ingredient is a bounded-cohomological stability theorem with an optimal range in degree three that…

We discuss graded D-brane systems of the topological A model on a Calabi-Yau threefold, by means of their string field theory. We give a detailed analysis of the extended string field action, showing that it satisfies the classical master…

We propose a new type of Dzyaloshinskii-Moriya (DM) interactions which act on high-rank multipolar moments such as quadrupolar and octupolar moments. Here we consider 5d1 systems with broken spatial inversion symmetry, where the interplay…

We use a 1-parameter version of gauge theory to investigate the topology of the diffeomorphism group of 4-manifolds. A polynomial invariant, analogous to the Donaldson polynomial, is defined, and is used to show that the diffeomorphism…

Chirality is an inherent characteristics of some objects in nature. In magnetism chiral magnetic textures can be formed in systems with broken inversion symmetry and due to an antisymmetric magnetic interaction, known as…

Let $3\leq d_1\leq d_2\leq d_3$ be integers. We show the following results: (1) If $d_2$ is a prime number and $\frac{d_1}{\gcd(d_1,d_3)}\neq2$, then $(d_1,d_2,d_3)$ is a multidegree of a tame automorphism if and only if $d_1=d_2$ or…

The goal of invariant theory is to find all the generators for the algebra of representations of a group that leave the group invariant. Such generators will be called \emph{basic invariants}. In particular, we set out to find the set of…

The aim of the present article is to construct quadratically integrable three dimensional systems in non-vanishing magnetic fields which possess so-called non-subgroup type integrals. The presence of such integrals means that the system…

The Sombor index (SO) is a vertex-degree-based graph invariant, defined as the sum over all pairs of adjacent vertices of $\sqrt{d_i^2+d_j^2}$, where $d_i$ is the degree of the $i$-th vertex. It has been conceived using geometric…

Gradient descent dynamics in complex energy landscapes, i.e. featuring multiple minima, finds application in many different problems, from soft matter to machine learning. Here, we analyze one of the simplest examples, namely that of soft…

Motivated by recent results in multiphoton interferometry, we expand a result of Kostant on immanants of an arbitrary $m\times m$ unitary matrix $T\in$ su$(m)$ to the submatrices of $T$. Specifically, we show that immanants of principal…