Related papers: Weyl Invariant Dynamics in 3 Dimensions

We consider three generalizations of the isoperimetric problem to higher codimension and provide results on equilibrium, stability, and minimization.

Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant polynomial. In this article we give a simple criterion…

Local Weyl modules over two-dimensional currents with values in $gl_r$ are deformed into spaces with bases related to parking functions. Using this construction we 1) propose a simple proof that dimension of the space of diagonal…

We investigate several integer invariants of curves in 3-space. We demonstrate relationships of these invariants to crossing number and to total curvature.

Variational-hemivariational inequalities are an area full of interesting and challenging mathematical problems. The area can be viewed as a natural extension of that of variational inequalities. Variational-hemivariational inequalities are…

Some aspects of the connection between differential geometry and multidimensional soliton equations are discussed.

We describe differential invariants of infinite-dimensional algebras being equivalence algebras of some classes of PDE and study structure of these algebras.

Quantum simulation of 1D relativistic quantum mechanics has been achieved in well-controlled systems like trapped ions, but properties like spin dynamics and response to external magnetic fields that appear only in higher dimensions remain…

We survey a number of Weyl type laws that have recently been established in low-dimensional symplectic geometry. These have had a number of applications, which we also introduce. We sketch a number of proofs so that the reader can get a…

We derive a Weyl invariant equation for Gravity by gauging the global Weyl invariance of vacuum Einstein equations. The equation is linear in the curvature and a natural generalization of Einstein equations to Weyl geometry. The system has…

In this paper, we consider the recovery of third-order differential operators from two spectra, as well as fourth-order or fifth-order differential operators from three spectra, where these differential operators are endowed with…

Weyl semimetals are a new class of Dirac material that posses bulk energy nodes in three dimensions. In this paper, we study a Weyl semimetal subject to an applied magnetic field. We derive expressions for the density of states, electronic…

Conventional quantization of two-dimensional diffeomorphism and Weyl invariant theories sacrifices the latter symmetry to anomalies, while maintaining the former. When alternatively Weyl invariance is preserved by abandoning diffeomorphism…

We use the integrable deformations method for a three-dimensional system of differential equations to obtain deformations of the T system. We analyze a deformation given by particular deformation functions. We point out that the obtained…

We consider the transmission problem for the Laplace equation on an infinite three-dimensional wedge, determining the complex parameters for which the problem is well-posed, and characterizing the infinite multiplicity nature of the…

On a (pseudo-) Riemannian manifold of dimension n > 2, the space of tensors which transform covariantly under Weyl rescalings of the metric is built. This construction is related to a Weyl-covariant operator D whose commutator [D,D] gives…

An extension to higher dimensions of the Bel-Debever characterization of the Weyl tensor is considered. This provides algebraic conditions that uniquely determine the multiplicity of a Weyl aligned null direction (WAND), and thus the…

We outline an abstract approach to the pseudo-differential Weyl calculus for operators in function spaces in infinitely many variables. Our earlier approach to the Weyl calculus for Lie group representations is extended to the case of…

Recent results on purely electric (PE) or magnetic (PM) spacetimes in n dimensions are summarized. These include: Weyl types; diagonalizability; conditions under which direct (or warped) products are PE/PM.

We describe the multiplicative invariant algebras of the root lattices of all irreducible root systems under the action of the Weyl group. In each case, a finite system of fundamental invariants is determined and the class group of the…