Related papers: Complete integrability versus symmetry
The sets used to construct other mathematical objects are pure sets, which means that all of their elements are sets, which are themselves pure. One set may therefore be within another, not as an element, but as an element of an element, or…
This article is concerned with perfect isometries between blocks of finite groups. Generalizing a method of Enguehard to show that any two p-blocks of (possibly different) symmetric groups with the same weight are perfectly isometric, we…
We give a brief overview of the Yangian symmetry of Feynman integrals. After a short introduction to the Yangian and integrability, we motivate the emergence of integrable structures for Feynman integrals via the fishnet limit of AdS/CFT.…
We show that the problem of counting perfect matchings remains #P-complete even if we restrict the input to very dense graphs, proving the conjecture in [5]. Here "dense graphs" refer to bipartite graphs of bipartite independence number…
It is shown that integrability is an accidental property of generic two-dimensional $O(2)$-symmetric asymptotically-free theories in the regime where the charge density is much larger than the dynamical scale. We show this by constructing…
We show the absence of continuous symmetry breaking in 2D lattice systems without any smoothness assumptions on the interaction. We treat certain cases of interactions with integrable singularities. We also present cases of singular…
In conformal field theory, the insertion of a defect breaks part of the global symmetry and gives rise to defect operators such as the tilts and displacements. We establish identities relating the integrated four-point functions of such…
We survey and compare, mainly in the two-dimensional case, various results obtained by IST and PDE techniques for integrable equations. We also comment on what can be predicted from integrable equations on non integrable ones.
It is shown that each integrable mapping is connected with a hierarchical completely integrable sytem of equations of evolution type which are invariant with respect to the transformation described by this mapping.
The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].
The notion of hidden symmetry algebra used in the context of exactly solvable systems is re-examined from the purely algebraic way, analyzing subspaces of commuting polynomials that generate finite-dimensional quadratic algebras. By…
Isometries of metric spaces $(X,d)$ preserve all level sets of $d$. We formulate and prove cases of a conjecture asserting if $X$ is a complete Riemannian manifold, then a function $f:X \rightarrow X$ preserving at least one level set…
We prove results about uniform convergence of densities in the free central limit theorem without assumptions of boundedness on the support.
We consider sets in uniformly perfect metric spaces which are null for every doubling measure of the space or which have positive measure for all doubling measures. These sets are called thin and fat, respectively. In our main results, we…
The concepts of differentiation and integration for matrices are known. As far as each matrix is differentiable, it is not clear a priori whether a given matrix is integrable or not. Recently some progress was obtained for diagonalizable…
The classical Cauchy completion of a metric space (by means of Cauchy sequences) as well as the completion of a uniform space (by means of Cauchy filters) are well-known to rely on the symmetry of the metric space or uniform space in…
The purpose of this paper is to develop a suitable notion of continuous L_infinity morphism between DG Lie algebras, and to study twists of such morphisms.
The standard definition of cylindrical symmetry in General Relativity is reviewed. Taking the view that axial symmetry is an essential pre-requisite for cylindrical symmetry, it is argued that the requirement of orthogonal transitivity of…
This paper introduces robust differential dynamic logic (a fragment of differential dynamic logic) to specify and reason about robust hybrid systems. Practically meaningful syntactic restrictions naturally ensure that definable properties…
We extend the notions of complete intersection dimension and lower complete intersection dimension to the category of complexes with finite homology and verify basic properties analogous to those holding for modules. We also discuss the…