Related papers: Composition structure of polyconvolution associate…
We expand correlation functions of the Langmann-Szabo-Zarembo (LSZ) model in terms of intersection numbers on the moduli space of complex curves. This provides an explicit, physically motivated example for the expansion of correlation…
We quantize a compactified version of the trigonometric Ruijse\-naars-Schneider particle model with a phase space that is symplectomorphic to the complex projective space CP^N. The quantum Hamiltonian is realized as a discrete difference…
The integrable structure of the two dimensional superconformal field theory is considered. The classical counterpart of our constructions is based on the $\hat{osp}(1|2)$ super-KdV hierarchy. The quantum version of the monodromy matrix…
Relations between triple Jordan systems and integrable multi-component models of the modified Korteveg--de Vries type are established. The most general model is related to a pair consisting of a triple Jordan system and a skew-symmetric…
We introduce an algebraic theory of integration on quantum planes and other braided spaces. In the one dimensional case we obtain a novel picture of the Jackson $q$-integral as indefinite integration on the braided group of functions in one…
Lagrangian multiforms provide a variational framework to describe integrable hierarchies. The case of Lagrangian $1$-forms covers finite-dimensional integrable systems. We use the theory of Lie dialgebras introduced by Semenov-Tian-Shansky…
An arbitrary-depth reduction theorem for the `convolution' multiple L-values of Euler-Zagier type is proven by an analytic method. To this end, generalized polylogarithms associated to Dirichlet characters are defined. The proof uses the…
Under the assumption that orthogonal polynomials of several variables admit an addition formula, we can define a convolution structure and use it to study the Fourier orthogonal expansions on a homogeneous space. We define a maximal…
This is a review of recent developments in the theory of beta ensembles of random matrices and their relations with conformal filed theory (CFT). There are (almost) no new results here. This article can serve as a guide on appearances and…
Soibelman's theory of quantized function algebra A_q(SL_n) provides a representation theoretical scheme to construct a solution of the Zamolodchikov tetrahedron equation. We extend this idea originally due to Kapranov and Voevodsky to…
There are well-known constructions of integrable systems which are chains of infinitely many copies of the equations of the KP hierarchy ``glued'' together with some additional variables, e.g., the modified KP hierarchy. Another…
The goal of this paper is to formalize the notion of The Compositional Integral in The Complex Plane. We prove a convergence theorem guaranteeing its existence. We prove an analogue of Cauchy's Integral Theorem--and suggest an approach at…
We give a rational surgery formula for the Casson-Walker invariant of a 2-component link in $S^{3}$ which is a generalization of Matveev-Polyak's formula. As application, we give more examples of non-hyperbolic L-space $M$ such that knots…
We study the Fourier orthogonal expansions with respect to the Laguerre type weigh functions on the conic surface of revolution and the domain bounded by such a surface. The main results include a closed form formula for the reproducing…
Let F(R^n) be the algebra of Fourier transforms of functions from L_1(R^n), K(R^n) be the algebra of Fourier transforms of bounded complex Borel measures in R^n and W be Wiener algebra of continuous 2pi-periodic functions with absolutely…
The Polchinski equations for the Wilsonian renormalization group in the $D$--dimensional matrix scalar field theory can be written at large $N$ in a Hamiltonian form. The Hamiltonian defines evolution along one extra holographic dimension…
We study one-dimensional functional inequalities of the type of Poincar\'e, logarithmic Sobolev and Wirtinger, with weight, for probability densities with polynomial tails. As main examples, we obtain sharp inequalities satisfied by inverse…
Recently, Rathie and K{\i}l{\i}\c{c}man (2014) employed Kummer-type transformation for $_{2}F_{2}(a, d+1; b, d; x)$ to develop certain classes of expansions theorems for $_{2}F_{2}(x)$ hypergeometric polynomial. Our aim is to deduce…
This is a continuation of our previous work 0712.4092. It is well known that various isoperimetric inequalities imply their functional ``counterparts'', but in general this is not an equivalence. We show that under certain convexity…
A classical result in quantum topology is that oriented 2-dimensional topological quantum field theories (2-TQFTs) are fully classified by commutative Frobenius algebras. In 2006, Turaev and Turner introduced additional structure on…