Published by Duke University Press since its inception in 1935, the Duke Mathematical Journal is one of the world's leading mathematical journals. Without specializing in a small number of subject areas, it emphasizes the most active and influential areas of current mathematics.

### Volume 153, Number 1

#### Publication Date: 15 May 2010

A dual characterization of the ${\mathcal C}^{1}$ harmonic capacity and applications

Albert Mas, Mark Melnikov and Xavier Tolsa; 1-22

Bass-Serre rigidity results in von Neumann algebras

Ionut Chifan and Cyril Houdayer; 23-54

Derived smooth manifolds

David I. Spivak; 55-128

Torelli theorem for graphs and tropical curves

Lucia Caporaso and Filippo Viviani; 129-171

Error estimates for the Davenport-Heilbronn theorems

Karim Belabas, Manjul Bhargava and Carl Pomerance; 173-210