相关论文: T-systems and the pentagram map

The (quantum) pentagon relation underlies the existing constructions of three dimensional quantum topology in the combinatorial framework of triangulations. Following the recent works \cite{KashaevLuoVartanov2012,AndersenKashaev2013}, we…

The pentagram map is a discrete dynamical system defined on the moduli space of polygons in the projective plane. This map has recently attracted a considerable interest, mostly because its connection to a number of different domains, such…

In this note we study the action of the pentagram map on the moduli space of twisted polygons. The action with respect to the canonical coordinate turns out to be applicable to the framework of tropical geometry. As an application, we…

This article discusses entanglement between two subsystems, one with discrete degrees of freedom and the other with continuous degrees of freedom. The overlap integral between continuous variable wave functions emerges as an important…

This article reviews a recently-discovered link between integrable quantum field theories and certain ordinary differential equations in the complex domain. Along the way, aspects of PT-symmetric quantum mechanics are discussed, and some…

The pentagram map is a discrete integrable system first introduced by Schwartz in 1992. It was proved to be intregable by Schwartz, Ovsienko, and Tabachnikov in 2010. Gekhtman, Shapiro, and Vainshtein studied Poisson geometry associated to…

Following the previous authors works (joint with I.A.Dynnikov) we develop a theory of the discrete analogs of the differential-geometrical (DG) connections in the triangulated manifolds. We study a nonstandard discretization based on the…

This talk gives an introduction into the subject of Seiberg-Witten curves and their relation to integrable systems. We discuss some motivations and origins of this relation and consider explicit construction of various families of…

The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…

The bases of the theory of integrals for multidimensional differential systems are stated. The integral equivalence of total differential systems, linear homogeneous systems of partial differential equations, and Pfaff systems of equations…

We derive a simple analytical expression for the level correlation function of an integrable system. It accounts for both the lack of correlations at smaller energy scales and for global rigidity (level number conservation) at larger…

In this article, we deal with several notions in dynamical systems. Firstly, we prove that both closure function and orbital function are idempotent on set-valued dynamical systems. And we show that the compact limit set of a connected set…

An argument is given to associate integrable nonintegrable transition of discrete maps with the transition of Lawvere's fixed point theorem to its own contrapositive. We show that the classical description of nonlinear maps is neither…

In this paper we derive from arguments of string scattering a set of eight tetrahedron equations, with different index orderings. It is argued that this system of equations is the proper system that represents integrable structures in three…

We record two facts on spaces of derived maps between the operads $E_d$ of little $d$-cubes. Firstly, these mapping spaces are equivalent to the mapping spaces between the non-unitary versions of $E_d$. Secondly, all endomorphisms of $E_d$…

We discuss the interrelations between symmetry of an Ito stochastic differential equations (or systems thereof) and its integrability, extending in party results by R. Kozlov [J. Phys. A ${\bf 43}$ (2010) \& ${\bf 44}$ (2011)]. Together…

We define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inverse problem for the discrete calculus of variation in the…

The T-systems and Y-systems are classes of algebraic relations originally associated with quantum affine algebras and Yangians. Recently the T-systems were generalized to quantum affinizations of a wide class of quantum Kac-Moody algebras…

We define higher pentagram maps on polygons in $P^d$ for any dimension $d$, which extend R.Schwartz's definition of the 2D pentagram map. We prove their integrability by presenting Lax representations with a spectral parameter for scale…

This paper considers a simple geometric construction, called the Pentagram map. The pentagram map, performed on N-gons, gives rise to a birational mapping on the space of all N-gons. This paper finds what conjecturally are all the…