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 129, Number 2

#### Publication Date: 15 August 2005

Nongenericity of variations of hodge structure for hypersurfaces of high degree

Emmanuel Allaud; 201-217

The torsion index of$E_8$ and other groups

Burt Totaro; 219-248

The torsion index of the spin groups

Burt Totaro; 249-290

V. Navarro, P. Pascual, A. Roig and F. Guillén Santos; 291-335

Mod ℓ representations of arithmetic fundamental groups, I: An analog of Serre's conjecture for function fields

Gebhard Böckle and Chandrashekhar Khare; 337-369

Rigidity and polynomial invariants of convex polytopes

Maksym Fedorchuk and Igor Pak; 371-404

Correction to “Gaps in $\sqrt{n}$ mod 1 and ergodic Theory”

Noam D. Elkies and Curtis T. Mcmullen; 405-406