Related papers: Rogers dilogarithm in integrable systems
We study the family of Y-systems and T-systems associated with the sine-Gordon models and the reduced sine-Gordon models for the parameter of continued fractions with two terms. We formulate these systems by cluster algebras, which turn out…
Present and future high-precision tests of the Standard Model and beyond for the fundamental constituents and interactions in Nature are demanding complex perturbative calculations involving multi-leg and multi-loop Feynman diagrams.…
Calculations using the (exact) fermionic functional renormalization group are usually truncated at the second order of the corresponding hierarchy of coupled ordinary differential equations. We present a method for the systematic…
Elements of the pomeron phenomenology within the Regge pole exchange picture are recalled. This includes discussion of the high energy behaviour of total cross-sections, the triple pomeron limit of the diffractive dissociation and the…
These are notes for my talk at ICCM 2010, Beijing. We survey some results, obtained jointly with Pavlo Pylyavskyy, concerning the ring of loop symmetric functions. Motivations from networks on surfaces, total positivity, crystal graphs, and…
These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. We start with a motivated introduction to the Langlands Program, including its geometric…
We introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their radii are described by a discrete integrable system. This is…
The geometric theory of Lie systems is used to establish integrability conditions for several systems of differential equations, in particular some Riccati equations and Ermakov systems. Many different integrability criteria in the…
Purely real space versions of the differential equations describing the kinematics of a dislocated crystalline medium are considered. The differential geometric structures associated with them are revealed.
Given a measured lamination on a finite area hyperbolic surface we consider a natural measure Mon the real line obtained by taking the push-forward of the volume measure of the unit tangent bundle of the surface under an intersection…
We give an exposition of fragments from Gauss [G] where he discovered, with the help of some work of Jacobi, a remarkable connection between Napier pentagons on the sphere and Poncelet pentagons on the plane. As a corollary we find a…
Algebraic integrability of the elliptic Calogero--Moser quantum problem related to the deformed root systems $\pbf{A_{2}(2)}$ is proved. Explicit formulae for integrals are found.
Hamiltonian systems with functionally dependent constraints (irregular systems), for which the standard Dirac procedure is not directly applicable, are discussed. They are classified according to their behavior in the vicinity of the…
We reprove the essential self-adjointness of the Dirichlet operators of Dirchlet forms for infinite particle systems with superstable and sub-exponentially decreasing interactions.
We discuss integrable many-body systems in one dimension of Calogero-Moser-Sutherland type, both classical and quantum as well as nonrelativistic and relativistic. In particular, we consider fundamental properties such as integrability, the…
In the present paper, as we did previously in [7], we investigate the relations between the geometric properties of tilings and the algebraic properties of associated relational structures. Our study is motivated by the existence of…
This paper addresses input-to-state stability (ISS) properties with respect to boundary and in-domain disturbances for a class of semi-linear partial differential equations (PDEs) subject to Dirichlet boundary conditions. The developed…
We derive the recurrence relations for relativistic Coulomb integrals directly from the integral representations with the help of computer algebra methods. In order to manage the computational complexity of this problem, we employ holonomic…
The relation between integrable systems and algebraic geometry is known since the XIXth century. The modern approach is to represent an integrable system as a Lax equation with spectral parameter. In this approach, the integrals of the…
We present a series of four self-contained lectures on the following topics: (I) An introduction to 4-dimensional 1\leq N \leq 4 supersymmetric Yang-Mills theory, including particle and field contents, N=1 and N=2 superfield methods and the…