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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, July 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
Related Articles
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 
On degenerations of moduli of Hitchin pairs
Volume 20, Number 0, Pages: 103  108, 2013
V. Balaji,
P. Barik
and D. S. Nagaraj
Abstract
References
Full Text
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The purpose of this note is to announce certain basic results on the construction of a degeneration of ${\mathcal{M}}_{{{X_{k}}}}^{{H}}(n,d)$ as the smooth curve $X_{k}$ degenerates to an irreducible nodal curve with a single node.

3 
Theory of $(a,b)$continued fraction transformations and applications
Volume 17, Number 0, Pages: 20  33, 2010
Svetlana Katok
and Ilie Ugarcovici
Abstract
Full Text
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We study a twoparameter family of onedimensional maps and the related $(a,b)$continued fractions suggested for consideration by Don Zagier and announce the following results and outline their proofs: (i) the associated natural extension maps
have attractors with finite rectangular structure for the entire parameter set except for a Cantorlike set of onedimensional zero measure that we completely describe; (ii) for a dense open set of parameters the Reduction theory conjecture holds, i.e. every point is mapped to the attractor after finitely many iterations.
We also give an application of this theory to coding geodesics on the modular surface and outline the computation of the smooth invariant measures associated with these transformations.

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 
Remarks on 5dimensional complete intersections
Volume 21, Number 0, Pages: 28  40, 2014
Jianbo Wang
Abstract
References
Full Text
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This paper will give some examples of diffeomorphic complex 5dimensional complete intersections and remarks on these examples. Then a result on the existence of diffeomorphic complete intersections that belong to components of the moduli space of different dimensions will be given as a supplement to the results of P.Brückmann (J. reine angew. Math. 476 (1996), 209215; 525 (2000), 213217).

6 
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.

7 
The spectral gap of graphs and Steklov eigenvalues on surfaces
Volume 21, Number 0, Pages: 19  27, 2014
Bruno Colbois
and Alexandre Girouard
Abstract
References
Full Text
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Using expander graphs, we construct a sequence
$\{\Omega_N\}_{N\in\mathbb{N}}$ of smooth compact surfaces with boundary of
perimeter $N$, and with the first nonzero Steklov
eigenvalue $\sigma_1(\Omega_N)$ uniformly bounded away from
zero. This answers a question which was raised in [10]. The
sequence $\sigma_1(\Omega_N) L(\partial\Omega_n)$ grows linearly with the genus of
$\Omega_N$, which is the optimal growth rate.

8 
The equivariant index theorem for
transversally elliptic operators and the basic index theorem for Riemannian
foliations
Volume 17, Number 0, Pages: 138  154, 2010
Jochen Brüning,
Franz W. Kamber
and Ken Richardson
Abstract
References
Full Text
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In this expository paper, we explain a formula for the multiplicities of the
index of an equivariant transversally elliptic operator on a $G$manifold.
The formula is a sum of integrals over blowups of the strata of the group
action and also involves eta invariants of associated elliptic operators.
Among the applications is an index formula for basic Dirac operators on
Riemannian foliations, a problem that was open for many years.

9 
Square function estimates in spaces of homogeneous type and on uniformly rectifiable Euclidean sets
Volume 21, Number 0, Pages: 8  18, 2014
Steve Hofmann,
Dorina Mitrea,
Marius Mitrea
and Andrew J. Morris
Abstract
References
Full Text
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We announce a local $T(b)$ theorem, an inductive scheme, and $L^p$ extrapolation
results for $L^2$ square function estimates related to the analysis of integral
operators that act on AhlforsDavid regular sets of arbitrary codimension in
ambient quasimetric spaces. The inductive scheme is a natural application of
the local $T(b)$ theorem and it implies the stability of $L^2$ square function
estimates under the socalled big pieces functor. In particular, this analysis
implies $L^p$ and Hardy space square function estimates for integral operators
on uniformly rectifiable subsets of the Euclidean space.

10 
New results on fat points schemes in $\mathbb{P}^2$
Volume 20, Number 0, Pages: 51  54, 2013
Marcin Dumnicki,
Tomasz Szemberg
and Halszka TutajGasińska
Abstract
References
Full Text
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The purpose of this note is to announce two results, Theorem A and Theorem B below, concerning geometric and algebraic properties of fat points in the complex projective plane. Their somewhat technical proofs are available in [10] and will be published elsewhere. Here we present only main ideas which are fairly transparent.

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