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Free to readers and authors, Electronic Research Announcements in Mathematical Sciences rapidly publishes announcements of significant advances in all branches of mathematics and short complete papers of original research (up to about 15 journal pages). Research announcements are an opportunity for lucid exposition of ideas and context unburdened by technical detail. All articles should be designed to communicate their contents to a broad mathematical audience and must meet high standards for mathematical content and clarity. After review and acceptance by the entire Editorial Board, articles enter production for immediate publication.
ERA is a continuation of Electronic Research Announcements of the AMS published by the American Mathematical Society from 1995 to the middle of 2007. After over two decades of leading this journal, Svetlana Katok became Founding Editor Emerita in January 2017.
 AIMS is a member of COPE. All AIMS journals adhere to the publication ethics and malpractice policies outlined by COPE.
 Publishes 1 issue a year.
 Publishes online only.
 Archived in Portico and CLOCKSS.
 ERAMS is a publication of the American Institute of Mathematical Sciences. All rights reserved.

TOP 10 Most Read Articles in ERAMS, November 2017
1 
Research announcement: The structure of groups with a quasiconvex hierarchy
Volume 16, Number 0, Pages: 44  55, 2009
Daniel T. Wise
Abstract
Full Text
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Let $G$ be a wordhyperbolic group with a quasiconvex hierarchy.
We show that $G$ has a finite index subgroup $G'$ that embeds as a
quasiconvex subgroup of a rightangled Artin group.
It follows that every quasiconvex subgroup of $G$ is a virtual retract,
and is hence separable.
The results are applied to certain 3manifold and onerelator groups.

2 
A characterization of the concept of duality
Volume 14, Number 0, Pages: 42  59,
Abstract
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3 
Realization of joint spectral radius via Ergodic theory
Volume 18, Number 0, Pages: 22  30, 2011
Xiongping Dai,
Yu Huang
and Mingqing Xiao
Abstract
References
Full Text
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Based on the classic multiplicative ergodic theorem and the semiuniform subadditive ergodic theorem, we show that there always exists at least one ergodic Borel probability measure such that
the joint spectral radius of a finite set of square matrices of the same size can be realized almost everywhere with respect to this Borel probability measure. The existence of at least one ergodic Borel probability measure, in the context of the joint spectral radius problem, is obtained in a general setting.

4 
Unboundedness of the Lagrangian Hofer distance in the Euclidean ball
Volume 21, Number 0, Pages: 1  7, 2014
Sobhan Seyfaddini
Abstract
References
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Let $\mathcal{L}$ denote the space of Lagrangians Hamiltonian isotopic to the standard Lagrangian in the unit ball in $\mathbb{R}^{2n}$. We prove that the Lagrangian Hofer distance on $\mathcal{L}$ is unbounded.

5 
Multifractal formalism derived from thermodynamics for general dynamical systems
Volume 17, Number 0, Pages: 1  11, 2010
Vaughn Climenhaga
Abstract
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We show that under quite general conditions, various multifractal spectra may be obtained as Legendre transforms of functions $T$: $ \RR\to \RR$ arising in the thermodynamic formalism. We impose minimal requirements on the maps we consider, and obtain partial results for any continuous map $f$ on a compact metric space. In order to obtain complete results, the primary hypothesis we require is that the functions $T$ be continuously differentiable. This makes rigorous the general paradigm of reducing questions regarding the multifractal formalism to questions regarding the thermodynamic formalism. These results hold for a broad class of measurable potentials, which includes (but is not limited to) continuous functions. Applications include most previously known results, as well as some new ones.

6 
Order isomorphisms in windows
Volume 18, Number 0, Pages: 112  118, 2011
Shiri ArtsteinAvidan,
Dan Florentin
and Vitali Milman
Abstract
References
Full Text
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We characterize order preserving transforms on the class of
lowersemicontinuous convex functions that are defined on a convex
subset of $\mathbb{R}^n$ (a "window") and some of its variants. To this
end, we investigate convexity preserving maps on subsets of $\mathbb{R}^n$.
We prove that, in general, an order isomorphism is induced by a
special convexity preserving point map on the epigraph of the
function. In the case of nonnegative convex functions on $K$, where
$0\in K$ and $f(0) = 0$, one may naturally partition the set of
order isomorphisms into two classes; we explain the main ideas
behind these results.

7 
A functional calculus in a noncommutative setting
Volume 14, Number 0, Pages: 60  68,
Abstract
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8 
Descent construction for GSpin groups: Main results and applications
Volume 16, Number 0, Pages: 30  36, 2009
Joseph Hundley
and Eitan Sayag
Abstract
Full Text
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The purpose of this note is to announce an extension of the
descent method of Ginzburg, Rallis, and Soudry to the setting of
essentially self dual representations. This extension of the
descent construction provides a complement to recent work of
Asgari and Shahidi [2]
on the generic transfer for general Spin groups as well as to the
work of Asgari and Raghuram [1] on cuspidality
of the exterior square lift for representations of $GL_4$.
Complete proofs of the results announced in the present note will
appear in our forthcoming article(s).

9 
New progress in nonuniform measure and cocycle rigidity
Volume 15, Number 0, Pages: 79  92,
Abstract
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10 
The approximate LoeblKomlósSós conjecture and embedding trees in sparse graphs
Volume 22, Number 0, Pages: 1  11, 2015
Jan Hladký,
Diana Piguet,
Miklós Simonovits,
Maya Stein
and Endre Szemerédi
Abstract
References
Full Text
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Loebl, Komlós and Sós conjectured that every $n$vertex graph $G$ with at least $n/2$ vertices
of degree at least $k$ contains each tree $T$ of order $k+1$ as a
subgraph. We give a sketch of a proof of the approximate version of this conjecture for large values of $k$.
For our proof, we use a structural decomposition which can be seen as an analogue of Szemerédi's regularity lemma for possibly very sparse graphs. With this tool, each graph can be decomposed into four parts: a set of vertices of huge degree, regular pairs (in the sense of the regularity lemma), and two other objects each exhibiting certain expansion properties. We then exploit the properties of each of the parts of $G$ to embed a given tree $T$.
The purpose of this note is to highlight the key steps of our proof. Details can be found in [arXiv:1211.3050].

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