Related papers: What is a hierarchically hyperbolic space?
The aim of this short survey is to advertise various tools that have been developed to study hierarchically hyperbolic spaces (HHSs) in recent years, with particular emphasis on those that require little to no knowledge of the HHS machinery…
This is a very short introduction to hierarchically hyperbolic spaces and groups. It is aimed at non-experts, including anyone who may encounter a group with some similarities to mapping class groups.
The first section of this modest survey reviews some basic notions and describes some families of examples, and the second section briefly indicates some general aspects of analysis on metric spaces. The remaining three sections are…
The combinatorial hierarchical hyperbolicity criterion is a very useful way of constructing new hierarchically hyperbolic spaces (HHSs). We show that, conversely, HHSs satisfying natural assumptions (satisfied, for example, by mapping class…
We introduce a number of tools for finding and studying \emph{hierarchically hyperbolic spaces (HHS)}, a rich class of spaces including mapping class groups of surfaces, Teichm\"{u}ller space with either the Teichm\"{u}ller or…
In this paper we consider a large family of graphs of hierarchically hyperbolic groups (HHG) and show that their fundamental groups admit HHG structures. To do that, we will investigate the notion of hierarchical quasi convexity and show…
This article simply presents several coordinate systems for 2 and 3-dimensional hyperbolic spaces, describing the general solutions of Helmholtz equation in each one of these systems.
This is a (very subjective) survey paper for nonspecialists covering group actions on Gromov hyperbolic spaces. The first section is about hyperbolic groups themselves, while the rest of the paper focuses on mapping class groups and…
This talk summarizes a method for analyzing the properties of any new scalar particle, which is systematic in the sense that it minimizes apriori theoretical assumptions about the properties of the scalar particle, leading to very…
This survey is a brief introduction to the theory of hyperbolic buildings and their lattices, with a focus on recent results.
Some of the guiding problems in partially hyperbolic systems are the following: (1) Examples, (2) Properties of invariant foliations, (3) Accessibility, (4) Ergodicity, (5) Lyapunov exponents, (6) Integrability of central foliations, (7)…
This article is a survey article on geometric group theory from the point of view of a non-expert who likes geometric group theory and uses it in his own research. The sections are: classical examples, basics about quasiisometry,properties…
An introduction to Hyperbolic Analysis is presented.
Recently, there has been a rising surge of momentum for deep representation learning in hyperbolic spaces due to theirhigh capacity of modeling data like knowledge graphs or synonym hierarchies, possessing hierarchical structure. We refer…
In this paper some concepts of convex analysis on hyperbolic space are studied. We first study properties of the intrinsic distance, for instance, we present the spectral decomposition of its Hessian. Next, we study the concept of convex…
Hierarchical Topic Models (HTMs) are useful for discovering topic hierarchies in a collection of documents. However, traditional HTMs often produce hierarchies where lowerlevel topics are unrelated and not specific enough to their…
Hierarchical semantic structures, naturally existing in real-world datasets, can assist in capturing the latent distribution of data to learn robust hash codes for retrieval systems. Although hierarchical semantic structures can be simply…
Hierarchically hyperbolic spaces (HHSs) are a large class of spaces that provide a unified framework for studying the mapping class group, right-angled Artin and Coxeter groups, and many 3--manifold groups. We investigate strongly…
Structuring latent representations in a hierarchical manner enables models to learn patterns at multiple levels of abstraction. However, most prevalent image understanding models focus on visual similarity, and learning visual hierarchies…
This first chapter intends to review and analyze the powerful new Harmony Search (HS) algorithm in the context of metaheuristic algorithms. I will first outline the fundamental steps of Harmony Search, and how it works. I then try to…