Related papers: Brief lectures on duality, integrability and defor…
In this article, we present a brief overview of some of the recent progress made in identifying and generating finite dimensional integrable nonlinear dynamical systems, exhibiting interesting oscillatory and other solution properties,…
We introduce two numerical conjugacy invariants for dynamical systems -- the complexity and weak complexity indices -- which are well-suited for the study of "completely integrable" Hamiltonian systems. These invariants can be seen as "slow…
Duality refers to two equivalent descriptions of the same theory from different points of view. Recently there has been tremendous progress in formulating and understanding possible dualities of quantum many body theories in $2+1$-spacetime…
These lectures present results and problems on the characterization of structurally stable dynamics. We will shed light those which do not seem to depend on the regularity class (holomorphic or differentiable). Furthermore, we will present…
In these lectures I review the general structure of electric--magnetic duality rotations in every even space--time dimension. In four dimensions, which is my main concern, I discuss the general issue of symplectic covariance and how it…
This is an introductory survey written in Japanese on classical integrability from the viewpoint of symmetry reduction of 4-dimensional anti-self-dual Yang-Mills equations. Twistor construction methods are discussed in detail in…
This paper proposes a modeling structure for the relativistic constitutive equations of inelastic deformation in materials moving at high speeds. While the theory of relativity has successfully approximated material motion in space-time,…
These lecture notes are devoted to the integrability of discrete systems and their relation to the theory of Yang-Baxter (YB) maps. Lax pairs play a significant role in the integrability of discrete systems. We introduce the notion of Lax…
We classify possible supersymmetry-preserving relevant, marginal, and irrelevant deformations of unitary superconformal theories in $d \geq 3$ dimensions. Our method only relies on symmetries and unitarity. Hence, the results are model…
The goal of these lectures is to present an informal but precise introduction to a body of concepts and methods of interest in number theory and string theory revolving around modular forms and their generalizations. Modular invariance lies…
An overview of some recent results on the geometry of partial differential equations in application to integrable systems is given. Lagrangian and Hamiltonian formalism both in the free case (on the space of infinite jets) and with…
In the first part of the thesis we construct models, called integrable, in which we can perform exact computations of physical quantities. We introduce several new out-of-equilibrium models that are obtained by solving, in specific cases,…
We present a large-scale (36000-particle) computational study of the "inherent structures" (IS) associated with equilibrium, two-dimensional, one-component Lennard-Jones systems. Our results provide strong support both for the…
We analyze in detail the possible breaking of spacetime supersymmetry under T-duality transformations. We find that when appropiate world-sheet effects are taken into account apparent puzzles concerning supersymmetry in spacetime are…
Non-trivial outer algebra automorphisms may be utilized in $\lambda$-deformations of (gauged) WZW models thus providing an efficient way to construct new integrable models. We provide two such integrable deformations of the exact coset CFT…
We consider a charged particle moving in a static electromagnetic field described by the vector potential $\vec A(\vec x)$ and the electrostatic potential $V(\vec x)$. We study the conditions on the structure of the integrals of motion of…
A model of relativistic extended particle is considered with the help of generalization of space-time inter-val. Ten additional dimensions are connected with six rotational and four deformational degrees of freedom. An obtained…
In these notes we review the S-matrix theory in (1+1)-dimensional integrable models, focusing mainly on the relativistic case. Once the main definitions and physical properties are introduced, we discuss the factorization of scattering…
In this lecture we address the following issues in the context of string theories: i) The role played by S and T dualities in obtaining topological inflation in N=1 supergravity models, ii) A mechanism to generate the baryon asymmetry of…
We study the integrability of two-dimensional theories that are obtained by a dimensional reduction of certain four-dimensional gravitational theories describing the coupling of Maxwell fields and neutral scalar fields to gravity in the…