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Free to all 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.

TOP 10 Most Read Articles in ERAMS, January 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 
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].

3 
A characterization of the concept of duality
Volume 14, Number 0, Pages: 42  59,
Abstract
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4 
Fixed frequency eigenfunction immersions and supremum norms of random waves
Volume 22, Number 0, Pages: 76  86, 2015
Yaiza Canzani
and Boris Hanin
Abstract
References
Full Text
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A compact Riemannian manifold may be immersed into Euclidean space by using high frequency Laplace eigenfunctions. We study the geometry of the manifold viewed as a metric space endowed with the distance function from the ambient Euclidean space. As an application we give a new proof of a result of BurqLebeau and others on upper bounds for the supnorms of random linear combinations of high frequency eigenfunctions.

5 
Global Kolmogorov tori in the planetary $\boldsymbol N$body problem. Announcement of result
Volume 22, Number 0, Pages: 55  75, 2015
Gabriella Pinzari
Abstract
References
Full Text
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We improve a result in [9] by proving the existence of a positive measure set of $(3n2)$dimensional quasiperiodic motions in the spacial, planetary $(1+n)$body problem away from coplanar, circular motions. We also prove that such quasiperiodic motions reach with continuity corresponding $(2n1)$dimensional ones of the planar problem, once the mutual inclinations go to zero (this is related to a speculation in [2]).
The main tool is a full reduction of the SO(3)symmetry, which retains symmetry by reflections and highlights a quasiintegrable structure, with a small remainder, independently of eccentricities and inclinations.

6 
Integration of exact Courant algebroids
Volume 19, Number 0, Pages: 58  76, 2012
David LiBland
and Pavol Ševera
Abstract
References
Full Text
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In this paper, we describe an integration of exact Courant algebroids to symplectic 2groupoids,
and we show that the differentiation procedure from [32] inverts our integration.

7 
A functional calculus in a noncommutative setting
Volume 14, Number 0, Pages: 60  68,
Abstract
Full Text
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8 
Smoothing 3dimensional polyhedral spaces
Volume 22, Number 0, Pages: 12  19, 2015
Nina Lebedeva,
Vladimir Matveev,
Anton Petrunin
and Vsevolod Shevchishin
Abstract
References
Full Text
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We show that 3dimensional polyhedral manifolds
with nonnegative curvature in the sense of Alexandrov
can be approximated by nonnegatively curved 3dimensional Riemannian manifolds.

9 
A sharp SobolevStrichartz estimate for the wave equation
Volume 22, Number 0, Pages: 46  54, 2015
Neal Bez
and Chris Jeavons
Abstract
References
Full Text
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We calculate the the sharp constant and characterize the extremal initial data in $\dot{H}^{\frac{3}{4}} \times \dot{H}^{\frac{1}{4}}$ for the $L^4$ SobolevStrichartz estimate for the wave equation in four spatial dimensions.

10 
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.

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