Related papers: Integrable Combinatorics
A problem with an instructive description of measurement process for sufficiently separated entangled quantum systems is well known. More precise and crafty experiments together with new technological challenges raise questions about…
We present a number of questions in commutative algebra posed on the problem solving seminar in algebra at Stockholm University during the period Fall 2014 - Spring 2017.
The following work is an exploration into certain topics in the broad world of integrable models, both classical and quantum, and consists of two main parts of roughly equal length. The first part, consisting of chapters 1-3, concerns…
In this talk we introduce several topics in combinatorial number theory which are related to groups; the topics include combinatorial aspects of covers of groups by cosets, and also restricted sumsets and zero-sum problems on abelian…
We give a sufficient condition for quantising integrable systems.
Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.
In this talk, I describe some recent ideas relating to the spectral reconstruction inverse problem, which arises frequently in lattice QCD calculations of inclusive hadronic quantities, and provide some physical context for this work.…
We review some essential aspects of classically integrable systems. The detailed outline of the lectures consists of: 1. Introduction and motivation, with historical remarks; 2. Liouville theorem and action-angle variables, with examples…
The structure and properties of possible $q$-Minkowski spaces is discussed, and the corresponding non-commutative differential calculi are developed in detail and compared with already existing proposals. This is done by stressing its…
We discuss a selection of recent developments in arithmetic combinatorics having to do with ``approximate algebraic structure'' together with some of their applications.
These notes are an expanded version of the lectures held in Tromso, in May 2025 at the "Lie-Stormer Summer School : Invariant Theory from classics to modern developments", in the framework of TiME events. We emphasize the analogy between…
Over the past twenty years, lecture hall partitions have emerged as fundamental combinatorial structures, leading to new generalizations and interpretations of classical theorems and new results. In recent years, geometric approaches to…
In these talks, I discuss a few selected topics in integrable models that are of interest from various points of view. Some open questions are also described.
We study some combinatorial and algebraic properties of certain quadratic algebras related with dynamical classical and classical Yang-Baxter equations. One can find more details about the content of present paper in Extended Abstract.
A review is given of the status and developments of the research program aiming to reformulate the physics of the four interactions at the classical level in a unified way in terms of Dirac-Bergmann observables with special emphasis on the…
This is an exposition of some new results on associated primes and the depth of different kinds of powers of monomial ideals in order to show a deep connection between commutative algebra and some objects in combinatorics such as simplicial…
These notes correspond to a mini-course given at the Poisson 2016 conference in Geneva. Starting from classical integrable systems in the sense of Liouville, we explore the notion of non-degenerate singularity and expose recent research in…
These are notes based on a series of talks that the author gave at the "Interactions between hyperbolic geometry and quantum groups" conference held at Columbia University in June of 2009.
Various aspects of the theory of quantum integrable systems are reviewed. Basic ideas behind the construction of integrable ultralocal and nonultralocal quantum models are explored by exploiting the underlying algebraic structures related…
We present the summary of the general discussion on the probabilistic foundations of quantum theory that took place during the round table at the Int. Conf. "Foundations of Probability and Physics", V\"axj\"o, Sweden-2000. It is possible to…