The infinite cyclohedron and its automorphism group

Cyclohedra are a well-known infinite familiy of finite-dimensional polytopes that can be constructed from centrally symmetric triangulations of even-sided polygons. In this article we introduce an infinite-dimensional analogue and prove that the group of symmetries of our construction is a semidirect product of a degree 2 central extension of Thompson's infinite finitely presented simple group T with the cyclic group of order 2. These results are inspired by a similar recent analysis by the first author of the automorphism group of an infinite-dimensional associahedron.Comment: 18 pages, 8 figure

Dynamics for holographic codes

We describe how to introduce dynamics for the holographic states and codes introduced by Pastawski, Yoshida, Harlow and Preskill. This task requires the definition of a continuous limit of the kinematical Hilbert space which we argue may be achieved via the semicontinuous limit of Jones. Dynamics is then introduced by building a unitary representation of a group known as Thompson's group T, which is closely related to the conformal group in 1+1 dimensions. The bulk Hilbert space is realised as a special subspace of the semicontinuous limit Hilbert space spanned by a class of distinguished states which can be assigned a discrete bulk geometry. The analogue of the group of large bulk diffeomorphisms is given by a unitary representation of the Ptolemy group Pt, on the bulk Hilbert space thus realising a toy model of the AdS/CFT correspondence which we call the Pt/T correspondence.Comment: 40 pages (revised version submitted to journal). See video of related talk: https://www.youtube.com/watch?v=xc2KIa2LDF

Manhattan orbifolds

We investigate a class of metrics for 2-manifolds in which, except for a discrete set of singular points, the metric is locally isometric to an L_1 (or equivalently L_infinity) metric, and show that with certain additional conditions such metrics are injective. We use this construction to find the tight span of squaregraphs and related graphs, and we find an injective metric that approximates the distances in the hyperbolic plane analogously to the way the rectilinear metrics approximate the Euclidean distance.Comment: 17 pages, 15 figures. Some definitions and proofs have been revised since the previous version, and a new example has been adde

Analytic Regularity for Linear Elliptic Systems in Polygons and Polyhedra

We prove weighted anisotropic analytic estimates for solutions of second order elliptic boundary value problems in polyhedra. The weighted analytic classes which we use are the same as those introduced by Guo in 1993 in view of establishing exponential convergence for hp finite element methods in polyhedra. We first give a simple proof of the known weighted analytic regularity in a polygon, relying on a new formulation of elliptic a priori estimates in smooth domains with analytic control of derivatives. The technique is based on dyadic partitions near the corners. This technique can successfully be extended to polyhedra, providing isotropic analytic regularity. This is not optimal, because it does not take advantage of the full regularity along the edges. We combine it with a nested open set technique to obtain the desired three-dimensional anisotropic analytic regularity result. Our proofs are global and do not require the analysis of singular functions.Comment: 54 page

Ethnonationalist Triads: Assessing the Influence of Kin Groups on Civil Wars

Although the case-based literature suggests that kin groups are prominent in ethnonationalist conflicts, quantitative studies of civil war onset have both overaggregated and underaggregated the role of ethnicity, by looking at civil war at the country level instead of among specific groups and by treating individual countries as closed units, ignoring groups' transnational links. In this article the authors integrate transnational links into a dyadic perspective on conflict between marginalized ethnic groups and governments. They argue that transnational links can increase the risk of conflict as transnational kin support can facilitate insurgencies and are difficult for governments to target or deter. The empirical analysis, using new geocoded data on ethnic groups on a transnational basis, indicates that the risk of conflict is high when large, excluded ethnic groups have transnational kin in neighboring countries, and it provides strong support for the authors' propositions on the importance of transnational ties in ethnonationalist conflict.</jats:p

A Local to Global Principle for the Complexity of Riemann Mappings (Extended Abstract)

We show that the computational complexity of Riemann mappings can be bounded by the complexity needed to compute conformal mappings locally at boundary points. As a consequence we get first formally proven upper bounds for Schwarz-Christoffel mappings and, more generally, Riemann mappings of domains with piecewise analytic boundaries