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Sequences that are defined by multisums of hypergeometric terms with compact support occur frequently in enumeration problems of combinatorics, algebraic geometry and perturbative quantum field theory. The standard recipe to study the…
A systematic and unified approach to transformations and symmetries of general second order linear parabolic partial differential equations is presented. Equivalence group is used to derive the Appell type transformations, specifically…
Symmetries play an essential role in the construction and phenomenology of quantum field theories (QFTs). We discuss how to construct symmetries of QFTs by extending minimal "seed" symmetry groups to larger groups that contain the seed(s)…
Homotopy is an important feature of associative and Jordan algebraic structures: such structures always come in families whose members need not be isomorphic among other, but still share many important properties. One may regard homotopy as…
Both symmetry and organized breaking of symmetry have a pivotal r\^ole in our understanding of structure and pattern formation in physical systems, including the origin of mass in the Universe and the chiral structure of biological…
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…
Symmetries have been exploited successfully within the realms of SAT and QBF to improve solver performance in practical applications and to devise more powerful proof systems. As a first step towards extending these advancements to the…
The reconstruction of fundamental parameters in supersymmetric theories requires the evolution to high scales, where the characteristic regularities in mechanisms of supersymmetry breaking become manifest. We have studied a set of…
We give technical conditions for a quasi-isometry of pairs to preserve a subgroup being hyperbolically embedded. We consider applications to the quasi-isometry and commensurability invariance of acylindrical hyperbolicity of finitely…
We propose a general construction principle which allows to include an infinite number of resonance states into a scattering matrix of hyperbolic type. As a concrete realization of this mechanism we provide new S-matrices generalizing a…
We consider the relationship between symmetries of two-dimensional autonomous dynamical system in two common formulations; as a set of differential equations for the derivative of each state with respect to time, and a single differential…
We produce examples of solutions to the non-abelian gravitating vortex equations, which are a dimensional reduction of the K\"aher-Yang-Mills- Higgs equations. These are equations for a K\"ahler metric and a metric on a vector bundle. We…
A type of prolongation structure for several general systems is discussed. They are based on a set of one-forms in which the underlying structure group of the integrability condition corresponds to the Lie-algebra of SL (2,R), O(3), or…
We consider geometric numerical integration algorithms for differential equations evolving on symmetric spaces. The integrators are constructed from canonical operations on the symmetric space, its Lie triple system (LTS), and the…
The construction of auxiliary matrices for the six-vertex model at a root of unity is investigated from a quantum group theoretic point of view. Employing the concept of intertwiners associated with the quantum loop algebra…
Symmetry problems in harmonic analysis are formulated and solved. One of these problems is equivalent to the refined Schiffer's conjecture which was recently proved by the author. Let $k=const>0$ be fixed, $S^2$ be the unit sphere in…
We propose $\hbar$-expansions as perturbative solutions of quantum extended Snyder and Yang models, with $\hbar$-independent classical zero-th order terms responsible for the spontaneous breaking of $D=4$ and $D=5$ de Sitter symmetries. In…
Exceptional points (EPs), at which both eigenvalues and eigenvectors coalesce, are ubiquitous and unique features of non-Hermitian systems. Second-order EPs are by far the most studied due to their abundance, requiring only the tuning of…
Following ideas of Iriyeh and Shibata we give a short proof of the three-dimensional Mahler conjecture {\mf for symmetric convex bodies}. Our contributions include, in particular, simple self-contained proofs of their two key statements.…
Spontaneous symmetry breaking is related to the appearance of emergent phenomena, while a non-vanishing order parameter has been viewed as the sign of turning into such symmetry breaking phase. Recently, we have proposed a continuous…