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We study locally compact convergence groups, in particular the link between the convergence property and the Specker compactifications (a genaralization of the ends) of a group.
Let G = SU(n,1), n >1 be the orientation-preserving isometry group of the complex hyperbolic space with an Iwasawa decomposition G = KAN. We prove local rigidity of a family of certain actions of a subgroup of AN on the imaginary boundary…
Motivated in part by understanding average case analysis of fundamental algorithms in computer science, and in part by the wide array of network data available over the last decade, a variety of random graph models, with corresponding…
We analyse the rigidity of discrete energies where at least nearest and next-to-nearest neighbour interactions are taken into account. Our purpose is to show that interactions beyond nearest neighbours have the role of penalising changes of…
In this work, we give a survey of recent developments in the theory of partial actions of groups and Hopf algebras.
We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the…
This paper is a follow-up to our joint paper with I. Agol, P. Storm and K. Whyte "Finiteness of arithmetic hyperbolic reflection groups". The main purpose is to investigate the effective side of the method developed there and its possible…
The formation of social networks and the evolution of their structures have been of interest to researchers for many decades. We wish to answer questions about network stability, group formation and popularity effects. We propose a latent…
We elucidate the dynamics of ongoing collective action among intentional agents with diverse beliefs and imperfect information. Their decisions on whether or not to contribute to the collective good depend not only on the past but also on…
We describe locally compact groups which are separably categorical metric structures. The paper extends (and corrects) Section 3 of the paper A.Ivanov, "Locally compact groups and continuous logic", arXiv: 1206.5473
This is an expository article on properties of actions on Lie groups by subgroups of their automorphism groups. After recalling various results on the structure of the automorphism groups, we discuss actions with dense orbits, invariant and…
In this paper, we extend the notion of temporo-spatial differentiation problems to the setting of actions of more general topological groups. The problem can be expressed as follows: Given an action $T$ of an amenable discrete group $G$ on…
In this article, we study several problems related to virtual traces for finite group actions on schemes of finite type over an algebraically closed field. We also discuss applications to fixed point sets. Our results generalize previous…
We give a survey of recent developments in the investigation of the various local-global conjectures for representations of finite groups.
This paper is a survey on the {\em Zimmer program}. In it's broadest form, this program seeks an understanding of actions of large groups on compact manifolds. The goals of this survey are $(1)$ to put in context the original questions and…
The theory of one-relator groups is now almost a century old. The authors therefore feel that a comprehensive survey of this fascinating subject is in order, and this document is an attempt at precisely such a survey. This article is…
Let $\Gamma$ be a weakly irreducible higher rank lattice. In this paper, we will prove various rigidity results for the $\Gamma$-action following a philosophy of the Zimmer program. We provide new rigidity results including local and global…
The main subject of the work is experimental investigation of local-time effect existence on laboratory scale, which means longitudinal distances between locations of measurements from tens to one meter. Also short revue of our…
Rodents serve as an important model for examining both individual and collective behavior. Dominance within rodent social structures can determine access to critical resources, such as food and mating opportunities. Yet, many aspects of the…
We introduce Schottky maps-conformal maps between relative Schottky sets, and study their local rigidity properties. This continues the investigations of relative Schottky sets initiated in [S. Merenkov, "Planar relative Schottky sets and…