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Mathematics of Computation

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

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Galois groups of Schubert problems via homotopy computation
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by Anton Leykin and Frank Sottile PDF
Math. Comp. 78 (2009), 1749-1765 Request permission

Abstract:

Numerical homotopy continuation of solutions to polynomial equations is the foundation for numerical algebraic geometry, whose development has been driven by applications of mathematics. We use numerical homotopy continuation to investigate the problem in pure mathematics of determining Galois groups in the Schubert calculus. For example, we show by direct computation that the Galois group of the Schubert problem of 3-planes in $\mathbb {C}^8$ meeting 15 fixed 5-planes non-trivially is the full symmetric group $S_{6006}$.
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Additional Information
  • Anton Leykin
  • Affiliation: Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 S. Morgan Street (M/C 249), Chicago, Illinois 60607-7045
  • MR Author ID: 687160
  • ORCID: 0000-0002-9216-3514
  • Email: leykin@math.uic.edu
  • Frank Sottile
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
  • MR Author ID: 355336
  • ORCID: 0000-0003-0087-7120
  • Email: sottile@math.tamu.edu
  • Received by editor(s): February 22, 2008
  • Received by editor(s) in revised form: June 14, 2008
  • Published electronically: February 25, 2009
  • Additional Notes: The authors were supported by the Institute for Mathematics and its Applications and Sottile by NSF grants CAREER DMS-0538734 and DMS-0701050
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 78 (2009), 1749-1765
  • MSC (2000): Primary 14N15, 65H20
  • DOI: https://doi.org/10.1090/S0025-5718-09-02239-X
  • MathSciNet review: 2501073