## 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. Advance publication of articles online is available.

On fluctuations of eigenvalues of random Hermitian matricesVolume 91, Number 1 (1998)
$v_n$ telescopes and the Adams spectral sequenceVolume 78, Number 1 (1995)
Subalgebras of infinite $C^\ast$ -algebras with finite Watatani indices, II: Cuntz-Krieger algebrasVolume 91, Number 3 (1998)
Finite group actions on C<sup>*</sup>-algebras with the Rohlin property, IVolume 122, Number 2 (2004)
Gamma classes and quantum cohomology of Fano manifolds: Gamma conjecturesVolume 165, Number 11 (2016)
• 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

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MR Citation Database MCQ (2015): 2.26
JCR (2015) Impact Factor: 2.350
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JCR (2015) Ranking: 9/312 (Mathematics)
Article Influence: 3.899
Eigenfactor: Duke Mathematical Journal
SJR/SCImago Journal Rank (2015): 5.675

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### Featured article

#### Gamma classes and quantum cohomology of Fano manifolds: Gamma conjectures

Volume 165, Number 11 (2016)
##### Abstract

We propose Gamma conjectures for Fano manifolds which can be thought of as a square root of the index theorem. Studying the exponential asymptotics of solutions to the quantum differential equation, we associate a principal asymptotic class $A_{F}$ to a Fano manifold $F$. We say that $F$ satisfies Gamma conjecture I if $A_{F}$ equals the Gamma class $\widehat{\Gamma}_{F}$. When the quantum cohomology of $F$ is semisimple, we say that $F$ satisfies Gamma conjecture II if the columns of the central connection matrix of the quantum cohomology are formed by $\widehat{\Gamma}_{F}\operatorname{Ch}(E_{i})$ for an exceptional collection $\{E_{i}\}$ in the derived category of coherent sheaves $\mathcal{D}^{b}_{\mathrm{coh}}(F)$. Gamma conjecture II refines a part of a conjecture by Dubrovin. We prove Gamma conjectures for projective spaces and Grassmannians.