Related papers: Research problems on relations between Nijenhuis g…
We describe a list of open problems in random matrix theory and the theory of integrable systems that was presented at the conference Asymptotics in Integrable Systems, Random Matrices and Random Processes and Universality, Centre de…
This is an expanded version of the lecture notes for a minicourse that I gave at a summer school called "Advanced Course on Geometry and Dynamics of Integrable Systems" at CRM Barcelona, 9--14/September/2013. In this text we study the…
This work is the first, and main, of the series of papers in progress dedicated to Nienhuis operators, i.e., fields of endomorphisms with vanishing Nijenhuis tensor. It serves as an introduction to Nijenhuis Geometry that should be…
We describe a list of open problems in random matrix theory and integrable systems which was presented at the conference ``Integrable Systems, Random Matrices, and Applications'' at the Courant Institute in May 2006.
Two discrete dynamical systems are discussed and analyzed whose trajectories encode significant explicit information about a number of problems in combinatorial probability, including graphical enumeration on Riemann surfaces and random…
A survey of some recent and important results which have to do with integrable equations and their relationship with the theory of surfaces is given. Some new results are also presented. The concept of the moving frame is examined, and it…
Geometric structures underlying commutative and non commutative integrable dynamics are analyzed. They lead to a new characterization of noncommutative integrability in terms of spectral properties and of Nijenhuis torsion of an invariant…
We study non-invariant Killing tensors with non-zero Nijenhuis torsion in the three-dimensional Euclidean space. Generalizing the corresponding integrable systems we construct two new families of superintegrable systems in $n$-dimensional…
This paper has been submitted to the Proceedings of the Australian-German Workshop on Differential Geometry in the Large held at the mathematical research institute MATRIX in Creswick, Victoria, Australia, Feb.2-Feb.14, 2019. We describe…
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…
The review studies connections between integrable many-body systems and gauge theories. It is shown how the degrees of freedom in integrable systems are related with topological degrees of freedom in gauge theories. The relations between…
We examine the metrics that arise when a finite set of points is embedded in the real line, in such a way that the distance between each pair of points is at least 1. These metrics are closely related to some other known metrics in the…
This contribution is based on a talk given by the author at the "Dualities and Generalized Geometries" session of the Corfu Summer Institute 2018 workshops. We overview the results of [1], focusing our attention on integrable…
This review article discusses recent progress in understanding of various families of integrable models in terms of algebraic geometry, representation theory, and physics. In particular, we address the connections between soluble many-body…
The aim of the paper is to present the integrable systems on partial isometries which are related to the restricted Grassmannian in finite dimensional context. Some explicit solutions are obtained.
The classical theory of $G$-structures, which include almost-complex structures, explains the relationship between the curvature of compatible connections and integrability. This note is an effort to understand how the curvature of…
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…
This thesis deals with the geometric and integrable aspects associated with random matrix models. Its purpose is to provide various applications of random matrix theory, from algebraic geometry to partial differential equations of…
We discuss basic features and new developments in recently proposed induced gauge theory solvable in any number of dimensions in the limit of infinite number of colours. Its geometrical (string) picture is clarified, using planar graph…
Hybrid systems are complex dynamical systems that combine discrete and continuous components. Reachability questions, regarding whether a system can run into a certain subset of its state space, stand at the core of verification and…