## 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.

On crystal bases of the $Q$ -analogue of universal enveloping algebrasVolume 63, Number 2 (1991)
Zeros of principal $L$ -functions and random matrix theoryVolume 81, Number 2 (1996)
Two-weight inequality for the Hilbert transform: A real variable characterization, IVolume 163, Number 15 (2014)
Limits for the characteristic roots of a matrixVolume 13, Number 3 (1946)
Decomposition rank of UHF-absorbing $\mathrm{C}^{*}$ -algebrasVolume 163, Number 14 (2014)
• 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.