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Scott Sheffield
Scott Sheffield (born October 20, 1973) is a professor of mathematics at the Massachusetts Institute of Technology.〔http://math.mit.edu/people/profile.php?pid=243, MIT, retrieved 2013-23-08.〕 His primary research field is theoretical probability.
==Research==
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.〔Conformal weldings of random surfaces: SLE and the quantum gravity zipper, Scott Sheffield, 2010, http://arxiv.org/abs/1012.4797〕 In joint work with Oded Schramm, he showed that contour lines of the Gaussian free field are related to SLE(4).〔Contour lines of the two-dimensional discrete Gaussian free field, Oded Schramm and Scott Sheffield, 2006, http://arxiv.org/abs/math/0605337〕〔A contour line of the continuum Gaussian free field, Oded Schramm and Scott Sheffield, 2010, http://arxiv.org/abs/1008.2447〕 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.〔Imaginary Geometry I: Interacting SLEs, Jason Miller and Scott Sheffield, 2012, http://arxiv.org/abs/1201.1496〕
Sheffield and Bertrand Duplantier proved the Knizhnik-Polyakov-Zamolodchikov (KPZ) relation for fractal scaling dimensions in Liouville quantum gravity.〔Liouville Quantum Gravity and KPZ, Bertrand Duplantier and Scott Sheffield, 2008, http://arxiv.org/abs/0808.1560〕 Sheffield also defined the conformal loop ensembles, which serve as scaling limits of the collection of all interfaces in various statistical physics models.〔Exploration trees and conformal loop ensembles, Scott Sheffield, 2006, http://arxiv.org/abs/math/0609167〕 In joint work with Wendelin Werner, he described the conformal loop ensembles as the outer boundaries of clusters of Brownian loops.〔Conformal loop ensembles: the Markovian characterization and loop soup construction, Scott Sheffield and Wendelin Werner, 2010, http://arxiv.org/abs/1006.2374〕
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.〔2011 Loève Prize announcement, http://www.stat.berkeley.edu/users/aldous/Research/sheffield.pdf〕
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