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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On entropy of spherical twists
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by Genki Ouchi; with an appendix by Arend Bayer PDF
Proc. Amer. Math. Soc. 148 (2020), 1003-1014 Request permission


In this paper, we compute categorical entropy of spherical twists. In particular, we prove that the Gromov–Yomdin-type conjecture holds for spherical twists. Moreover, we construct counterexamples of Gromov–Yomdin type conjecture for K3 surfaces modifying Fan’s construction for even higher-dimensional Calabi–Yau manifolds.

The appendix, by Arend Bayer, shows the nonemptiness of complements of a number of spherical objects in the derived categories of K3 surfaces.

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Additional Information
  • Genki Ouchi
  • Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, Meguro-ku, Tokyo 153-8914, Japan
  • Address at time of publication: RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program, 2F Main Research Building, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
  • MR Author ID: 1205200
  • Email:
  • Arend Bayer
  • Affiliation: School of Mathematics and Maxwell Institute, University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, United Kingdom
  • MR Author ID: 728427
  • Email:
  • Received by editor(s): September 27, 2017
  • Received by editor(s) in revised form: July 9, 2019
  • Published electronically: October 18, 2019
  • Additional Notes: This work was supported by Grant-in-Aid for JSPS Research Fellow 15J08505.
  • Communicated by: Lev Borisov
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 148 (2020), 1003-1014
  • MSC (2010): Primary 14F05
  • DOI:
  • MathSciNet review: 4055930