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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Schubert calculus and torsion explosion
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by Geordie Williamson; with a joint appendix with Alex Kontorovich; with a joint appendix with Peter J. McNamara PDF
J. Amer. Math. Soc. 30 (2017), 1023-1046 Request permission


The author observes that certain numbers occurring in Schubert calculus for $\text {SL}_n$ also occur as entries in intersection forms controlling decompositions of Soergel bimodules in higher rank. These numbers grow exponentially. This observation gives many counter-examples to the expected bounds in Lusztig’s conjecture on the characters of simple rational modules for $\text {SL}_n$ over fields of positive characteristic. The examples also give counter-examples to the James conjecture on decomposition numbers for symmetric groups.
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Additional Information
  • Geordie Williamson
  • Affiliation: Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111, Bonn, Germany
  • MR Author ID: 845262
  • Email:
  • Alex Kontorovich
  • Affiliation: Rutgers University, New Brunswick, New Jersey
  • MR Author ID: 704943
  • ORCID: 0000-0001-7626-8319
  • Email:
  • Peter J. McNamara
  • Affiliation: University of Queensland, Brisbane, Queensland, Australia
  • MR Author ID: 791816
  • Email:
  • Received by editor(s): June 22, 2015
  • Received by editor(s) in revised form: May 5, 2016, and August 4, 2016
  • Published electronically: October 20, 2016
  • Additional Notes: The first author of the Appendix is partially supported by an NSF CAREER grant DMS-1455705 and an Alfred P. Sloan Research Fellowship.

  • Dedicated: Dedicated to Meg and Gong.
  • © Copyright 2016 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 30 (2017), 1023-1046
  • MSC (2010): Primary 20C20, 20G05; Secondary 14N15, 14M15
  • DOI:
  • MathSciNet review: 3671935