Related papers: Modified Tetrahedron Equations and Related 3D Inte…
We discuss a system of third order PDEs for strictly convex smooth functions on domains of Euclidean space. We argue that it may be understood as a closure of sorts of the first order prolongation of a family of second order PDEs. We…
We explicitly construct K-theoretic and elliptic stable envelopes for certain moduli spaces of vortices, and apply this to enumerative geometry of rational curves in these varieties. In particular, we identify the quantum difference…
The tetrahedron equation arises as a generalization of the famous Yang--Baxter equation to the 2+1-dimensional quantum field theory and the 3-dimensional statistical mechanics. Very little is still known about its solutions. Here a…
We consider the problem of obtaining higher order in regularization parameter $\epsilon$ analytical results for master integrals with elliptics. The two commonly employed methods are provided by the use of differential equations and direct…
We introduce and study matrix transfers to achieve elementary models for bivariant $K$-theory. They share lots of common properties with Voevodsky's framed correspondences and lead to symmetric matrix motives of algebraic varieties…
The focus in this paper is on elliptic homogenization of a certain kind of possibly non-periodic problems. A non-periodic and two-dimensional example is studied, where we numerically illustrate the homogenized matrix.
Reciprocal matrices are tridiagonal matrices $(a_{ij})_{i,j=1}^n$ with constant main diagonal and such that $a_{i,i+1}a_{i+1,i}=1$ for $i=1,\ldots,n-1$. For these matrices, criteria are established under which their Kippenhahn curves…
We prove a transformation formula relating two determinants involving elliptic shifted factorials. Similar determinants have been applied to multiple elliptic hypergeometric series.
We introduce a new technique for constructing three-dimensional (3D) models of incompressible Riemann S-type ellipsoids and compressible triaxial configurations that share the same velocity field as that of Riemann S-type ellipsoids. Our…
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…
Kaneko and Sakai recently observed that certain elliptic curves whose associated newforms (by the modularity theorem) are given by the eta-quotients can be characterized by a particular differential equation involving modular forms and…
We construct $2^n$-families of solutions of the Yang-Baxter equation from $n$-products of three-dimensional $R$ and $L$ operators satisfying the tetrahedron equation. They are identified with the quantum $R$ matrices for the Hopf algebras…
A multiparametric extension of the anisotropic U model is discussed which maintains integrability. The R-matrix solving the Yang-Baxter equation is obtained through a twisting construction applied to the underlying Uq(sl(2|1))…
The description of complex physical phenomena often involves sophisticated models that rely on a large number of parameters, with many dimensions and scales. One practical way to simplify that kind of models is to discard some of the…
A new family of analytically solvable quantum geometric models is proposed. The structure of the energy spectra as well as the form of the corresponding eigenfunctions are presented pointing out their main specific properties.
For two-dimensional lattice equations one definition of integrability is that the model can be naturally and consistently extended to three dimensions, i.e., that it is "consistent around a cube" (CAC). As a consequence of CAC one can…
We study operators on a singular manifold, here of conical or edge type, and develop a new general approach of representing asymptotics of solutions to elliptic equations close to the singularities. The idea is to construct so-called…
We show that well-posed, conformally-decomposed formulations of the 3+1 Einstein equations can be obtained by densitizing the lapse and by combining the constraints with the evolution equations. We compute the characteristics structure and…
We discuss the notion of matrix model, $\pi:C(X)\to M_K(C(T))$, for algebraic submanifolds of the free complex sphere, $X\subset S^{N-1}_{\mathbb C,+}$. When $K\in\mathbb N$ is fixed there is a universal such model, which factorizes as…
Multidimensional matrix inversions provide a powerful tool for studying multiple hypergeometric series. In order to extend this technique to elliptic hypergeometric series, we present three new multidimensional matrix inversions. As…