The Compositio Prize is a prize awarded every third year by the Foundation Compositio Mathematica in recognition of an outstanding piece of mathematical research that is published in the Compositio Mathematica journal.

Full prize details

Below is a directory to past winners of the prize. The winning papers for the period 2017-2019, The K3 category of a cubic fourfold and Local Langlands correspondence and ramification for Carayol representations, are free to access through 31st December 2022.

Compositio Prize for the period 2017-2019

The K3 category of a cubic fourfold
Daniel Huybrechts
Volume 153, Issue 3 (2017)

The article The K3 category of a cubic fourfold by Daniel Huybrechts establishes a collection of important results about Kuznetsov components of smooth cubic fourfolds. The Kuznetsov component is a subcategory of the derived category. Huybrechts proves that for a smooth cubic fourfold X, there are only finitely many isomorphism classes of fourfolds whose Kuznetsov component is Fourie--Mukai equivalent to that of X, and only one such class when X is very general. It also gives a criterion for the Kuznetsov component to be equivalent to the derived category of a twisted K3 surface. This influential article should pave the way to solving the mysterious rationality problem for cubic fourfolds.

Local Langlands correspondence and ramification for Carayol representations
Colin J. Bushnell and Guy Henniart
Volume 155, Issue 10 (2019)

The article Local Langlands correspondence and ramification for Carayol representations by Colin Bushnell and Guy Henniart constitutes major progress in the study of local Langlands.The authors establish a complete classification of Herbrand functions arising from totally wild simple characters of Carayol type. They use this to completely describe the ramification behaviour of the corresponding Weil group representations.

Compositio Prize for the period 2014-2016

Dense clusters of primes in subsets
James Maynard
Volume 152, Issue 7 (2016)

Compositio Prize for the period 2011-2013

Derived splinters in positive characteristic
Bhargav Bhatt
Volume 148, Issue 6 (2012)

Compositio Prize winner for the period 2008-2010

Le lemme fondamental pondéré. I. Constructions géométriques
P-H. Chaudouard, G. Laumon
Volume 146, Issue 6 (2010)

Compositio Prize winner for the period 2005-2007

Gromov-Witten theory and Donaldson-Thomas theory, II
D. Maulik, N. Nekrasov, A. Okounkov, R. Pandharipande
Volume 142, Issue 5 (2006)

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