Related papers: Geodesic rewriting systems and pregroups

Geometric methods proposed by Stallings for treating finitely generated subgroups of free groups were successfully used by many authors to solve a wide collection of decision problems for free groups and their subgroups. In the present…

We study Hamiltonian reductions of the free geodesic motion on a non-compact simple Lie group using as reduction group the direct product of a maximal compact subgroup and the fixed point subgroup of an arbitrary involution commuting with…

A problem of recent interest has been to study how large subsets of the natural numbers can be while avoiding 3-term geometric progressions. Building on recent progress on this problem, we consider the analogous problem over quadratic…

In this note we show that for any hyperbolic surface S, the number of geodesics of length bounded above by L in the mapping class group orbit of a fixed closed geodesic with a single double point is asymptotic to L raised to the dimension…

This is the written version of the Bourbaki seminar given in January 2013 and published in 2014 (modulo an additional early reference added subsequently). It describes the first construction of infinite, finitely generated amenable simple…

We propose a general convex optimization problem for computing regularized geodesic distances. We show that under mild conditions on the regularizer the problem is well posed. We propose three different regularizers and provide analytical…

This paper is a survey, with few proofs, of ideas and notions related to self-similarity of groups, semi-groups and their actions. It attempts to relate these concepts to more familiar ones, such as fractals, self-similar sets, and…

We consider the structures given by repeatedly generalising the definition of finite state automata by symmetry considerations, and constructing analogues of transition monoids at each step. This approach first gives us non-deterministic…

We develop a new thermodynamic approach to stochastic graph-rewriting. The ingredients are a finite set of reversible graph-rewriting rules called generating rules, a finite set of connected graphs P called energy patterns and an energy…

We present a careful approximation of the geodesics in trees of hyperbolic or relatively hyperbolic groups. As an application we prove a combination theorem for finite graphs of relatively hyperbolic groups, with both Farb's and Gromov's…

Given a transitive permutation group, a fundamental object for studying its higher transitivity properties is the permutation action of its isotropy subgroup. We reverse this relationship and introduce a universal construction of infinite…

In this paper, we survey constructions of and nonexistence results on combinatorial/geometric structures which arise from unions of cyclotomic classes of finite fields. In particular, we survey both classical and recent results on…

In this paper we examine a number of term rewriting system for integer number representations, building further upon the datatype defining systems described in [2]. In particular, we look at automated methods for proving confluence and…

Algorithms for minimal enclosing ball problems are often geometric in nature. To highlight the metric ingredients underlying their efficiency, we focus here on a particularly simple geodesic-based method. A recent subgradient-based study…

Computing geodesics for Riemannian manifolds is a difficult task that often relies on numerical approximations. However, these approximations tend to be either numerically unstable, have slow convergence, or scale poorly with manifold…

We consider here a generalization of a well known discrete dynamical system produced by the bisection of reflection angles that are constructed recursively between two lines in the Euclidean plane. It is shown that similar properties of…

Developed by Buchberger for commutative polynomial rings, Groebner Bases are frequently applied to solve algorithmic problems, such as the congruence problem for ideals. Until now, these ideas have been transmitted to different in part…

We construct convex bodies that can be "captured by nets." More precisely, for each dimension $n \geq 2$, we construct a family of Riemannian $n$-spheres, each with a stable geodesic net, which is a stable 1-dimensional integral varifold.…

The equations of motion of a charged ideal fluid, respectively the superconductivity equation (both in a given magnetic field) are showed to be geodesic equations on a general, respectively central extension of the group of volume…

We develop a general model theoretic semantics to rewriting beyond the usual confluence and termination assumptions. This is based on preordered algebra which is a model theory that extends many sorted algebra. In this framework we…