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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Conformal invariance and $2D$ statistical physics
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by Gregory F. Lawler PDF
Bull. Amer. Math. Soc. 46 (2009), 35-54 Request permission


A number of two-dimensional models in statistical physics are conjectured to have scaling limits at criticality that are in some sense conformally invariant. In the last ten years, the rigorous understanding of such limits has increased significantly. I give an introduction to the models and one of the major new mathematical structures, the Schramm-Loewner Evolution ($SLE$).
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Additional Information
  • Gregory F. Lawler
  • Affiliation: Department of Mathematics, University of Chicago, 5734 S. University Ave., Chicago, Illinois 60637-1546
  • MR Author ID: 111050
  • Email:
  • Received by editor(s): June 20, 2008
  • Published electronically: September 22, 2008
  • Additional Notes: This research was supported by National Science Foundation grant DMS-0734151
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Bull. Amer. Math. Soc. 46 (2009), 35-54
  • MSC (2000): Primary 82B27; Secondary 30C35, 60J65, 82B27
  • DOI:
  • MathSciNet review: 2457071