Volume 169 Issue 1 – January 2009

The `Harder-Narasimhan trace’ and unitarity of the KZ/Hitchin connection: genus 0

Pages 1-39 by Trivandrum Ramakrishnan Ramadas | From volume 169-1

Regularity of flat level sets in phase transitions

Pages 41-78 by Ovidiu Savin | From volume 169-1

Existence of Engel structures

Pages 79-137 by Thomas Vogel | From volume 169-1

Stable manifolds for an orbitally unstable nonlinear Schrödinger equation

Pages 139-227 by Wilhelm Schlag | From volume 169-1

On Serre’s conjecture for 2-dimensional mod p representations of $\mathrm{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})$

Pages 229-253 by Chandrashekhar Khare, Jean-Pierre Wintenberger | From volume 169-1

Holomorphic curves into algebraic varieties

Pages 255-267 by Min Ru | From volume 169-1

Finite groups of symplectic automorphisms of K3 surfaces in positive characteristic

Pages 269-313 by Igor Dolgachev, JongHae Keum | From volume 169-1

Fitting a $C^m$-smooth function to data, I

Pages 315-346 by Charles Fefferman, Bo'az Klartag | From volume 169-1