Related papers: Integrable Combinatorics
We provide five rearticulations of the thesis that the structure of spacetime is conventional, rather than empirically determined, based upon variation of the structures that are empirically underdetermined and modal contexts in which this…
This paper is an extended version of a series of lectures on polar spaces given during the workshop and conference 'Groups and Geometries', held at the Indian Statistical Institute in Bangalore in December 2012. The aim of this paper is to…
We consider colored compositions where only some parts are allowed different colors, depending on their locations in the composition. The counting sequences are obtained through generating functions. Connections to many other combinatorial…
This paper, written in relation to the Current Developments in Mathematics 2012 Conference, discusses the recent papers on perfectoid spaces. Apart from giving an introduction to their content, it includes some open questions, as well as…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
The question of how irreversibility can emerge as a generic phenomena when the underlying mechanical theory is reversible has been a long-standing fundamental problem for both classical and quantum mechanics. We describe a mechanism for the…
Properties of partial integrals such as real and complex-valued polynomial, multiple polynomial, exponential, and conditional for ordinary differential systems are studied. The possibilities of constructing first integrals and last…
This paper is for the proceedings of the Chen-Chow Conference held in Tianjin, China in October 2000. The goal of the paper is to produce and survey evidence for a connection between Chen's work on iterated integrals on the one hand, and…
A problem of constructing quantum groups from classical r-matrices is discussed.
We describe recent attempts at discretizing canonical quantum gravity in four dimensions in terms of a connection formulation. This includes a general introduction, a comparison between the real and complex connection approach, and a…
This textbook, "Counting Rocks!", is the written component of an interactive introduction to combinatorics at the undergraduate level. Throughout the text, we link to videos where we describe the material and provide examples. The major…
A new realist interpretation of quantum mechanics is introduced. Quantum systems are shown to have two kinds of properties: the usual ones described by values of quantum observables, which are called extrinsic, and those that can be…
We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…
Observables in a quantum system, represented by a Hilbert space, are given by the orthogonal bases of the aforementioned Hilbert space. Categorical Quantum Mechanics provides further abstraction of such observables, allowing for a…
We give integral presentations of quantum lattice Heisenberg algebras by viewing them as Heisenberg doubles. Our presentations generalize those appearing previously in the literature.
We embark on a tour that takes us through four closely related topics: the dual concepts of independence and spanning in finite abelian groups and the analogous dual concepts of designs and distance sets on spheres. We review some of the…
The optimal matching of point clouds in $\mathbb{R}^d$ is a combinatorial problem; applications in statistics motivate to consider random point clouds, like the Poisson point process. There is a crucial dependance on dimension $d$, with…
The new millennium's qualitative advances in relativistic heavy ion physics are in part due to, and are in part causing, a new appreciation for quantitative rigor in both experimental and theoretical work in the field. In these proceedings…
This article is a survey of classical and quantum completely integrable systems from the viewpoint of local ``phase space'' analysis. It advocates the use of normal forms and shows how to get global information from glueing local pieces.…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.