Volume 175 Issue 3 – May 2012

## Local entropy averages and projections of fractal measures

Pages 1001-1059 by Michael Hochman, Pablo Shmerkin

## Replica symmetry of the minimum matching

Pages 1061-1091 by Johan Wästlund

## The dimension and structure of the space of harmonic 2-spheres in the $m$-sphere

Pages 1093-1125 by Luis Fernández

## Immersing almost geodesic surfaces in a closed hyperbolic three manifold

Pages 1127-1190 by Jeremy Kahn, Vladimir Markovic

## The embedding capacity of $4$-dimensional symplectic ellipsoids

Pages 1191-1282 by Dusa McDuff, Felix Schlenk

## A new proof of the density Hales-Jewett theorem

Pages 1283-1327 by D. H. J. Polymath

## Topology of Hitchin systems and Hodge theory of character varieties: the case $A_1$

Pages 1329-1407 by Mark Andrea A. de Cataldo, Tamás Hausel, Luca Migliorini

## Cover times, blanket times, and majorizing measures

Pages 1409-1471 by Jian Ding, James R. Lee, Yuval Peres

## The sharp weighted bound for general Calderón–Zygmund operators

Pages 1473-1506 by Tuomas P. Hytönen

## On sharp transitions in making squares

Pages 1507-1550 by Ernie Croot, Andrew Granville, Robin Pemantle, Prasad Tetali

## Nonlinear wave equations as limits of convex minimization problems: proof of a conjecture by De Giorgi

Pages 1551-1574 by Enrico Serra, Paolo Tilli

## Vinogradov’s mean value theorem via efficient congruencing

Pages 1575-1627 by Trevor D. Wooley

## Bounds for the multiplicities of cohomological automorphic forms on $\mathrm{GL}_2$

Pages 1629-1651 by Simon Marshall

## The connective constant of the honeycomb lattice equals $\sqrt{2+\sqrt 2}$

Pages 1653-1665 by Hugo Duminil-Copin, Stanislav Smirnov

## Norm convergence of nilpotent ergodic averages

Pages 1667-1688 by Miguel N. Walsh