## Duke Mathematical Journal

Published by Duke University Press since its inception in 1935, the Duke Mathematical Journal is one of the world's leading mathematical journals. DMJ emphasizes the most active and influential areas of current mathematics.

The ergodic theoremVolume 5, Number 1 (1939)
The variation of spectraVolume 18, Number 1 (1951)
Harmonic Maass forms of weight $1$Volume 164, Number 1 (2015)
A formal power series operational calculus for quasinilpotent operatorsVolume 38, Number 4 (1971)
The special values of the zeta functions associated with Hilbert modular formsVolume 45, Number 3 (1978)
• ISSN: 0012-7094 (print), 1547-7398 (electronic)
• Publisher: Duke University Press
• Discipline(s): Mathematics
• Full text available in Euclid: 1935 --
• Access: By subscription only
• Euclid URL: http://projecteuclid.org/dmj

### Featured article

#### Symmetric differentials and the fundamental group

Volume 162, Number 14
##### Abstract

We show that any smooth complex projective variety whose fundamental group has a complex representation with infinite image must have a nonzero symmetric differential (a section of a symmetric power of the cotangent bundle). Along the way, we produce many symmetric differentials on the base of a variation of Hodge structures.