Volume 171

## The classification of Kleinian surface groups, I: models and bounds

Pages 1-107 by Yair Minsky | From volume 171-1

## Uniqueness for the signature of a path of bounded variation and the reduced path group

Pages 109-167 by Ben Hambly, Terry Lyons | From volume 171-1

## Transformations of elliptic hypergeometric integrals

Pages 169-243 by Eric M. Rains | From volume 171-1

## Mirković-Vilonen cycles and polytopes

Pages 245-294 by Joel Kamnitzer | From volume 171-1

## Noise stability of functions with low influences: Invariance and optimality

Pages 295-341 by Elchanan Mossel, Ryan O’Donnell, Krzysztof Oleszkiewicz | From volume 171-1

## Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces

Pages 343-373 by Vitali Kapovitch, Anton Petrunin, Wilderich Tuschmann | From volume 171-1

## On the classification of finite-dimensional pointed Hopf algebras

Pages 375-417 by Nicolás Andruskiewitsch , Hans-Jürgen Schneider | From volume 171-1

## Dyson’s ranks and Maass forms

Pages 419-449 by Kathrin Bringmann, Ken Ono | From volume 171-1

## On the ergodicity of partially hyperbolic systems

Pages 451-489 by Keith Burns, Amie Wilkinson | From volume 171-1

## The Smith-Toda complex $V((p+1)/2)$ does not exist

Pages 491-509 by Lee S. Nave | From volume 171-1

## The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields

Pages 511-532 by Bjorn Poonen, José Felipe Voloch | From volume 171-1

## Essential dimension, spinor groups, and quadratic forms

Pages 533-544 by Patrick Brosnan, Zinovy Reichstein, Angelo Vistoli | From volume 171-1

## Pentagon and hexagon equations

Pages 545-556 by Hidekazu Furusho | From volume 171-1

## A nonhomogeneous orbit closure of a diagonal subgroup

Pages 557-570 by François Maucourant | From volume 171-1

## Tight closure does not commute with localization

Pages 571-588 by Holger Brenner, Paul Monsky | From volume 171-1

## Characterization of Lee-Yang polynomials

Pages 589-603 by David Ruelle | From volume 171-1

## Ergodic billiards that are not quantum unique ergodic (with an appendix by Andrew Hassell and Luc Hillairet)

Pages 605-618 by Andrew Hassell, Luc Hillairet | From volume 171-1

## Quantitative noise sensitivity and exceptional times for percolation

Pages 619-672 by Oded Schramm, Jeffrey E. Steif | From volume 171-2

## Free boundaries in optimal transport and Monge-Ampère obstacle problems

Pages 673-730 by Luis Caffarelli, Robert J. McCann | From volume 171-2

## The cohomology ring of the real locus of the moduli space of stable curves of genus $0$ with marked points

Pages 731-777 by Pavel Etingof, André Henriques, Joel Kamnitzer, Eric M. Rains | From volume 171-2

## A family of Calabi-Yau varieties and potential automorphy

Pages 779-813 by Michael Harris, Nick Shepherd-Barron, Richard Taylor | From volume 171-2

## Arithmetic quantum unique ergodicity for symplectic linear maps of the multidimensional torus

Pages 815-879 by Dubi Kelmer | From volume 171-2

## A group-theoretic approach to a family of $2$-local finite groups constructed by Levi and Oliver

Pages 881-978 by Michael Aschbacher, Andrew Chermak | From volume 171-2

## Polynomial parametrization for the solutions of Diophantine equations and arithmetic groups

Pages 979-1009 by Leonid Vaserstein | From volume 171-2

## Constructible exponential functions, motivic Fourier transform and transfer principle

Pages 1011-1065 by Raf Cluckers, François Loeser | From volume 171-2

## Global solutions of shock reflection by large-angle wedges for potential flow

Pages 1067-1182 by Gui-Qiang Chen, Mikhail Feldman | From volume 171-2

## Boundary rigidity and filling volume minimality of metrics close to a flat one

Pages 1183-1211 by Dmitri Burago, Sergei Ivanov | From volume 171-2

## An algorithm for computing some Heegaard Floer homologies

Pages 1213-1236 by Sucharit Sarkar, Jiajun Wang | From volume 171-2

## Order of current variance and diffusivity in the asymmetric simple exclusion process

Pages 1237-1265 by Márton Balázs , Timo Seppäläinen | From volume 171-2

## Quantization of coboundary Lie bialgebras

Pages 1267-1345 by Benjamin Enriquez, Gilles Halbout | From volume 171-2

## Differentiating maps into $L^1$, and the geometry of $\rm BV$ functions

Pages 1347-1385 by Jeff Cheeger, Bruce Kleiner | From volume 171-2

Pages 1387-1400 by Lewis Phylip Bowen | From volume 171-2

## The global stability of Minkowski space-time in harmonic gauge

Pages 1401-1477 by Hans Lindblad, Igor Rodnianski | From volume 171-3

## Divergent square averages

Pages 1479-1530 by Zoltán Buczolich , R. Daniel Mauldin | From volume 171-3

## Un indice qui affine l’indice de Poincaré-Lefschetz pour les homeomorphismes de surfaces

Pages 1531-1589 by Frédéric Le Roux | From volume 171-3

## Sur un problème de Gelfond : la somme des chiffres des nombres premiers

Pages 1591-1646 by Christian Mauduit, Joël Rivat | From volume 171-3

## The Atiyah-Singer index formula for subelliptic operators on contact manifolds. Part I

Pages 1647-1681 by Erik van Erp | From volume 171-3

## The Atiyah-Singer index formula for subelliptic operators on contact manifolds. Part II

Pages 1683-1706 by Erik van Erp | From volume 171-3

## Cones and gauges in complex spaces: Spectral gaps and complex Perron-Frobenius theory

Pages 1707-1752 by Hans Henrik Rugh | From volume 171-3

## Linear equations in primes

Pages 1753-1850 by Ben Green, Terence Tao | From volume 171-3

## Measure equivalence rigidity of the mapping class group

Pages 1851-1901 by Yoshikata Kida | From volume 171-3

## Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation

Pages 1903-1930 by Luis Caffarelli, Alexis Vasseur | From volume 171-3

## Perturbations of orthogonal polynomials with periodic recursion coefficients

Pages 1931-2010 by David Damanik, Rowan Killip, Barry Simon | From volume 171-3

## A characterization of the entropies of multidimensional shifts of finite type

Pages 2011-2038 by Michael Hochman, Tom Meyerovitch | From volume 171-3

## Vacant set of random interlacements and percolation

Pages 2039-2087 by Alain-Sol Sznitman | From volume 171-3

## The perverse filtration and the Lefschetz hyperplane theorem

Pages 2089-2113 by Mark Andrea A. de Cataldo, Luca Migliorini | From volume 171-3

## Densities for rough differential equations under Hörmander’s condition

Pages 2115-2141 by Thomas Cass, Peter Friz | From volume 171-3

## Some adjoints in homotopy categories

Pages 2143-2155 by Amnon Neeman | From volume 171-3

## Insufficiency of the Brauer-Manin obstruction applied to étale covers

Pages 2157-2169 by Bjorn Poonen | From volume 171-3

## Cappell-Shaneson homotopy spheres are standard

Pages 2171-2175 by Selman Akbulut | From volume 171-3