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We determine and analyze maximally supersymmetric configurations in four-dimensional gauged N=2 supergravity, preserving eight supercharges. These models include arbitrary electric gaugings in the vector- and hypermultiplet sectors. We…
Hyperbolic lattices are a new type of synthetic quantum matter emulated in circuit quantum electrodynamics and electric-circuit networks, where particles coherently hop on a discrete tessellation of two-dimensional negatively curved space.…
In this paper, a supersymmetric extension of the polytropic gas dynamics equations is constructed through the use of a superspace involving two independent fermionic variables and two bosonic superfields. A superalgebra of symmetries of the…
We review the construction of higher-form symmetries for supersymmetric theories using a supergeometry framework. This reveals an enlarged set of topological conserved supercurrents, including Chern-Weil symmetries and new geometric…
Extending the supersymmetric method proposed by Tkachuk to the complex domain, we obtain general expressions for superpotentials allowing generation of quasi-exactly solvable PT-symmetric potentials with two known real eigenvalues (the…
In recent work, two of the authors proposed a broad global well-posedness conjecture for cubic quasilinear dispersive equations in two space dimensions, which asserts that global well-posedness and scattering holds for small initial data in…
In this paper we discuss a method of generating supersymmetric solutions of the Einstein equations. The method involves the embedding of one supersymmetric spacetime into another. We present two examples with constituent spacetimes which…
For any n\ge 2, we give infinitely many unsplittable links of n components in the 3-sphere which admit non-trivial surgery yielding the 3-sphere again and whose components are mutually distinct hyperbolic knots. Berge and Kawauchi gave…
The supersymmetrical approach is used to analyse a class of two-dimensional quantum systems with periodic potentials. In particular, the method of SUSY-separation of variables allowed us to find a part of the energy spectra and the…
The transition between two conceptionally different solution procedures for general axisymmetric tangential contact problems with arbitrary laoding histories under Hertz-Mindlin assumptions is demonstrated, namely J\"ager's superposition…
Models of interactions of D-dimensional hypermultiplets and supersymmetric gauge multiplets with $\mathcal{N}=8$ supercharges $(D{\leq} 6)$ can be formulated in the framework of harmonic superspaces. The effective Coulomb low-energy action…
We develop classical globally supersymmetric theories. As much as possible, we treat various dimensions and various amounts of supersymmetry in a uniform manner. We discuss theories both in components and in superspace. Throughout we…
In this paper a new supersymmetric extension of conformal mechanics is put forward. The beauty of this extension is that all variables have a clear geometrical meaning and the super-Hamiltonian turns out to be the Lie-derivative of the…
In the framework of multiple-scattering theory, we show that the dispersion relations of certain electromagnetic (EM) and elastic metamaterials can be obtained analytically in the long-wavelength limit. Specific examples are given to the…
We present SU$(2|1)$ supersymmetric mechanics on $n$-dimensional Riemannian manifolds within the Hamiltonian approach. The structure functions including prepotentials entering the supercharges and the Hamiltonian obey extended curved WDVV…
We present in this paper a rather general method for the construction of so-called conditionally exactly solvable potentials. This method is based on algebraic tools known from supersymmetric quantum mechanics. Various families of…
We investigate the geometry of hyperbolic knots and links whose diagrams have a high amount of twisting of multiple strands. We find information on volume and certain isotopy classes of geodesics for the complements of these links, based…
We construct new solutions in series of confluent hypergeometric functions for the confluent Heun equation (CHE). Some of these solutions are applied to the one-dimensional stationary Schr\"{o}dinger equation with hyperbolic and…
Among the usual constraints of (1,1) supergravity in d=2 the condition of vanishing bosonic torsion is dropped. Using the inverse supervierbein and the superconnection considerably simplifies the formidable computational problems. It allows…
Solving tangle equations is deeply connected with studying enzyme action on DNA. The main goal of this paper is to solve the system of tangle equations $N(O+X_1)=b_1$ and $N(O+X_2)=b_2 \# b_3$, where $X_1$ and $X_2$ are rational tangles,…