Volume 170 Issue 3 – November 2009

## Optimality and uniqueness of the Leech lattice among lattices

Pages 1003-1050 by Henry Cohn, Abhinav Kumar | From volume 170-3

## Proper affine actions and geodesic flows of hyperbolic surfaces

Pages 1051-1083 by William M. Goldman, François Labourie, Gregory Margulis | From volume 170-3

## Moduli of finite flat group schemes, and modularity

Pages 1085-1180 by Mark Kisin | From volume 170-3

## Strong cosmic censorship in $T^{3}$-Gowdy spacetimes

Pages 1181-1240 by Hans Ringström | From volume 170-3

## On the decomposition of global conformal invariants, I

Pages 1241-1306 by Spyros Alexakis | From volume 170-3

## Donaldson-Thomas type invariants via microlocal geometry

Pages 1307-1338 by Kai Behrend | From volume 170-3

## Localization of $\mathfrak g$-modules on the affine Grassmannian

Pages 1339-1381 by Edward Frenkel, Dennis Gaitsgory | From volume 170-3

## Word maps, conjugacy classes, and a noncommutative Waring-type theorem

Pages 1383-1416 by Aner Shalev | From volume 170-3

## The Euler equations as a differential inclusion

Pages 1417-1436 by Camillo De Lellis, László Székelyhidi Jr. | From volume 170-3

## Bounds for multiplicities of unitary representations of cohomological type in spaces of cusp forms

Pages 1437-1446 by Frank Calegari, Matthew Emerton | From volume 170-3

## Subgroups of direct products of limit groups

Pages 1447-1467 by Martin R. Bridson, James Howie, Charles F. Miller III, Hamish Short | From volume 170-3

## A rigid irregular connection on the projective line

Pages 1469-1512 by Edward Frenkel, Benedict Gross | From volume 170-3