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Recently it was shown that mirror duals of 3d and 4d theories with four super-charges can be described by generalized quiver theories, constructed using strongly coupled SCFTs as elementary building blocks that replace and improve standard…
Triple stars and compact objects are ubiquitously observed in nature. Their long-term evolution is complex; in particular, the von-Zeipel-Lidov-Kozai (ZLK) mechanism can potentially lead to highly eccentric encounters of the inner binary.…
We review a geometrical, so called superembedding, approach to the description of the dynamics of point-like and extended supersymmetric objects (superbranes) in String Theory. The approach is based on a supersymmetric extension of the…
We study the geometry of elliptic fibrations given by Weierstrass models resulting from Step 6 of Tate's algorithm. Such elliptic fibrations have a discriminant locus containing an irreducible component $S$, over which the generic fiber is…
Functional relation for commuting quantum transfer matrices of quantum integrable models is identified with classical Hirota's bilinear difference equation. This equation is equivalent to the completely discretized classical 2D Toda lattice…
The superstatistics concept is a useful statistical method to describe inhomogeneous complex systems for which a system parameter $\beta$ fluctuates on a large spatio-temporal scale. In this paper we analyze a measured time series of wind…
We discuss the role of string solitons in duality and examine the feature of compositeness, which allows for the interpretation of general solutions as bound states of supersymmetric fundamental constituents. This feature lies at the heart…
The duality cascade, and its dual description as string theory on the warped deformed conifold, brings together several sophisticated topics, some of which are not widely known. These lectures, which contain a number of previously…
One-dimensional and two-dimensional integrals containing $E_b(-u)$ and $E_{\alpha ,\beta }\left(\delta x^{\gamma }\right)$ are considered. $E_b(-u)$ is the Mittag-Leffler function and the integral is taken over the rectangle $0 \leq x <…
Stochastic perturbations (radial) of a spherically symmetric relativistic star, modeled by a perfect fluid in comoving coordinates for the collapse scenario are worked out using the classical Einstein- Langevin equation, which has been…
Let $f:[0,+\infty) \to \mathbb{R}$ be a (locally) Lipschitz function and $\Omega \subset \mathbb{R}^2$ a $C^{1,\alpha}$ domain whose boundary is unbounded and connected. If there exists a positive bounded solution to the overdetermined…
The symmetries provided by representations of the centrally extended Lie superalgebra $\mathfrak{psl}(2|2)$ are known to play an important role in the spin chain models originated in the planar anti-de Sitter/conformal field theory…
The temperature inversion properties of the internal energy, E, on odd spheres, and its derivatives, together with their expression in elliptic terms, as expounded in previous papers, are extended to the integrals of E, thence making…
Recently we proposed a generic construction of the additional integrals of motion for the St\"ackel systems applying addition theorems to the angle variables. In this note we show some trivial examples associated with angle variables for…
We access the edge of Gaussian beta ensembles with one spike by analyzing high powers of the associated tridiagonal matrix models. In the classical cases beta=1, 2, 4, this corresponds to studying the fluctuations of the largest eigenvalues…
We study the system $-\Delta \mathbf{u}=| \mathbf{u}|^{\alpha-1} \mathbf{u}$ with $1<\alpha\leq\frac{n+2}{n-2}$, where $ \mathbf{u}=(u_1,\dots,u_m)$, $m\geq 1$, is a $C^2$ nonnegative function that develops an isolated singularity in a…
The unparalleled photometric data obtained by NASA's Kepler Space Telescope has led to improved understanding of red-giant stars and binary stars. We discuss the characterization of known eccentric system, containing a solar-like…
In this work we extend the results of previous derivations of Seiberg-like dualities (level-rank duality) between gauged Wess-Zumino-Witten theories. The arguments in use to identify a potential dual for the supersymmetric WZW theory based…
A new Hilbert-type integral inequality in the whole plane with the non-homogeneous kernel and parameters is given. The constant factor related to the hypergeometric function and the beta function is proved to be the best possible. As…
We start from an interpretation of the $BC_2$-symmetric "Type I" (elliptic Dixon) elliptic hypergeometric integral evaluation as a formula for a Casoratian of the elliptic hypergeometric equation, and give an extension to higher-dimensional…