Related papers: Matrix Models, Complex Geometry and Integrable Sys…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
We describe a simple algebraic approach to several spectral duality results for integrable systems and illustrate the method for two types of examples: The Bertola-Eynard-Harnad spectral duality of the two-matrix model as well as the…
A master equation expressing the classical integrability of two-dimensional non-linear sigma models is found. The geometrical properties of this equation are outlined. In particular, a closer connection between integrability and T-duality…
Exactly integrable systems connected to semisimple algebras of second rank with an arbitrary choice of grading are presented in explicit form. General solutions of these systems are expressed in terms of matrix elements of two fundamental…
In these lecture notes we review the various relations between intersection theory on the moduli space of Riemann surfaces, integrable hierarchies of KdV type, matrix models, and topological quantum field theories. We explain in particular…
In this paper, we present a unified analysis of matrix completion under general low-dimensional structural constraints induced by {\em any} norm regularization. We consider two estimators for the general problem of structured matrix…
Matrix hierarchies are: multi-component KP, general Zakharov-Shabat (ZS) and its special cases, e.g., AKNS. The ZS comprises all integrable systems having a form of zero-curvature equations with rational dependence of matrices on a spectral…
We discuss various aspects of most general multisupport solutions to matrix models in the presence of hard walls, i.e., in the case where the eigenvalue support is confined to subdomains of the real axis. The structure of the solution at…
This monograph, written for educational purposes, serves as an introduction to the concept of integrability as it applies to systems of differential equations (both ordinary and partial) as well as to vector-valued fields. The general cases…
We present an intuitive diagrammatic representation of a new class of integrable $\s$-models. It is shown that to any given diagram corresponds an integrable theory that couples $N$ WZW models with a certain number of each of the following…
Tropical Geometry and Mathematical Morphology share the same max-plus and min-plus semiring arithmetic and matrix algebra. In this chapter we summarize some of their main ideas and common (geometric and algebraic) structure, generalize and…
We study glued tensor and free products of compact matrix quantum groups with cyclic groups -- so-called tensor and free complexifications. We characterize them by studying their representation categories and algebraic relations. In…
In factoring matrices into the product of two matrices operations are typically performed with elements restricted to matrix subspaces. Such modest structural assumptions are realistic, for example, in large scale computations. This paper…
In the recent years a lot of attention is focused on unconventional string compactifications. A variety of different but related frameworks was developed in order to address issues such as duality invariance, non-geometry and…
We consider principal fibre bundles with a given connection and construct almost complex structures on the total space if the adjoint bundle is isomorphic to the tangent bundle of the base. We derive the integrability condition. If the…
We study associative multiplications in semi-simple associative algebras over C compatible with the usual one. An interesting class of such multiplications is related to the affine Dynkin diagrams of A, D, E-type. In this paper we…
A notion of dual curve for pseudoholomorphic curves in 4--manifolds turns out to be possible only if the notion of almost complex structure structure is slightly generalized. The resulting structure is as easy (perhaps easier) to work with,…
In this paper, we investigate the Euler-type integral representations for the generalized hypergeometric matrix function and develop some transformations in terms of hypergeometric matrix functions. Furthermore, unit and half arguments have…
We build and investigate a pure gauge theory on arbitrary discrete groups. A systematic approach to the construction of the differential calculus is presented. We discuss the metric properties of the models and introduce the action…
Using unitarity methods, we compute, for several massive two-dimensional models, the cut-constructible part of the one-loop 2->2 scattering S-matrices from the tree-level amplitudes. We apply our method to various integrable theories,…