Scott Sheffield


Scott Sheffield (born October 20, 1973) is a professor of mathematics at the Massachusetts Institute of Technology.[1] His primary research field is theoretical probability.

Scott Sheffield
Scott Sheffield.jpg
Born (1973-10-20) October 20, 1973 (age 48)
Alma materStanford University
AwardsLoève Prize (2011)
Rollo Davidson Prize (2006)
Clay Research Award (2017)
Scientific career
ThesisRandom surfaces: large deviations and gradient Gibbs measure classifications (2003)
Doctoral advisorAmir Dembo
Doctoral studentsEwain Gwynne, Nina Holden, Xin Sun


Much of Sheffield's work examines conformal invariant objects which arise in the study of two-dimensional statistical physics models. He studies the Schramm-Loewner evolution SLE(κ) and its relations to a variety of other random objects. For example, he proved that SLE describes the interface between two Liouville quantum gravity surfaces that have been conformally welded together.[2] In joint work with Oded Schramm, he showed that contour lines of the Gaussian free field are related to SLE(4).[3][4] With Jason Miller, he developed the theory of Gaussian free field flow lines, which include SLE(κ) for all values of κ, as well as many variants of SLE.[5]

Sheffield and Bertrand Duplantier proved the Knizhnik-Polyakov-Zamolodchikov (KPZ) relation for fractal scaling dimensions in Liouville quantum gravity.[6] Sheffield also defined the conformal loop ensembles, which serve as scaling limits of the collection of all interfaces in various statistical physics models.[7] In joint work with Wendelin Werner, he described the conformal loop ensembles as the outer boundaries of clusters of Brownian loops.[8]

In addition to these contributions, Sheffield has also proved results regarding internal diffusion limited aggregation, dimers, game theory, partial differential equations, and Lipschitz extension theory.[9]


Since 2011, Sheffield has taught 18.600 (formerly 18.440), the introductory probability course at MIT.[10]

Education and careerEdit

Sheffield graduated from Harvard University in 1998 with an A.B. and A.M. in mathematics. In 2003, he received his Ph.D. in mathematics from Stanford University. Before becoming a professor at MIT, Sheffield held postdoctoral positions at Microsoft Research, the University of California at Berkeley, and the Institute for Advanced Study. He was also an associate professor at New York University.[11]


Scott Sheffield received the Loève Prize, the Presidential Early Career Award for Scientists and Engineers, the Sloan Research Fellowship, and the Rollo Davidson Prize. He was also an invited speaker at the 2010 meeting of the International Congress of Mathematicians. In 2017 he received the Clay Research Award jointly with Jason Miller.[12] He was elected to the American Academy of Arts and Sciences in 2021.[13]


  • Scott Sheffield (2005), Random Surfaces, American Mathematical Society[14]


  1. ^ "Scott Sheffield". Retrieved December 12, 2021.
  2. ^ Sheffield, Scott (2010). "Conformal weldings of random surfaces: SLE and the quantum gravity zipper". arXiv:1012.4797. {{cite journal}}: Cite journal requires |journal= (help)
  3. ^ Schramm, Oded; Sheffield, Scott (2006). "Contour lines of the two-dimensional discrete Gaussian free field". arXiv:math/0605337. Bibcode:2006math......5337S. {{cite journal}}: Cite journal requires |journal= (help)
  4. ^ Schramm, Oded; Sheffield, Scott (2010). "A contour line of the continuum Gaussian free field". arXiv:1008.2447. {{cite journal}}: Cite journal requires |journal= (help)
  5. ^ Miller, Jason; Sheffield, Scott (2012). "Imaginary Geometry I: Interacting SLEs". arXiv:1201.1496. {{cite journal}}: Cite journal requires |journal= (help)
  6. ^ Duplantier, Bertrand; Sheffield, Scott (2008). "Liouville Quantum Gravity and KPZ". arXiv:0808.1560. {{cite journal}}: Cite journal requires |journal= (help)
  7. ^ Sheffield, Scott (2006). "Exploration trees and conformal loop ensembles". arXiv:math/0609167. Bibcode:2006math......9167S. {{cite journal}}: Cite journal requires |journal= (help)
  8. ^ Sheffield, Scott; Werner, Wendelin (2010). "Conformal Loop Ensembles: The Markovian characterization and the loop-soup construction". arXiv:1006.2374. {{cite journal}}: Cite journal requires |journal= (help)
  9. ^ 2011 Loève Prize announcement,
  10. ^
  11. ^ "CV". MIT. Retrieved August 23, 2013.
  12. ^ Clay Research Award 2017
  13. ^ "New Members Elected in 2021". American Academy of Arts and Sciences. Retrieved April 22, 2021.
  14. ^ Sheffield, Scott (2005). Random surfaces. Société mathématique de France. p. vi+175. ISBN 2856291872. Retrieved September 21, 2019.