Scott Sheffield (born October 20, 1973) is a professor of

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

at the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...

. 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. In joint work with Oded Schramm, he showed that contour lines of the

Gaussian free field In probability theory and statistical mechanics, the Gaussian free field (GFF) is a Gaussian random field, a central model of random surfaces (random height functions). gives a mathematical survey of the Gaussian free field. The discrete version ...

are related to SLE(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. Sheffield and Bertrand Duplantier proved the Knizhnik-Polyakov-Zamolodchikov (KPZ) relation for fractal scaling dimensions in Liouville quantum gravity. Sheffield also defined the conformal loop ensembles, which serve as scaling limits of the collection of all interfaces in various statistical physics models. In joint work with

Wendelin Werner Wendelin Werner (born 23 September 1968) is a German-born French mathematician working on random processes such as self-avoiding random walks, Brownian motion, Schramm–Loewner evolution, and related theories in probability theory and mathematica ...

, he described the conformal loop ensembles as the outer boundaries of clusters of Brownian loops. In addition to these contributions, Sheffield has also proved results regarding internal

diffusion limited aggregation Diffusion-limited aggregation (DLA) is the process whereby particles undergoing a random walk due to Brownian motion cluster together to form aggregates of such particles. This theory, proposed by T.A. Witten Jr. and L.M. Sander in 1981, is app ...

, dimers,

game theory Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...

partial differential equations In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to ...

, and Lipschitz extension theory.

Teaching

Since 2011, Sheffield has taught 18.600 (formerly 18.440), the introductory probability course at MIT. Sheffield was a visiting professor at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

for the 2022 to 2023 academic year.

Education and career

Sheffield graduated from

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

in 1998 with an A.B. and A.M. in mathematics. In 2003, he received his Ph.D. in mathematics from

Stanford University Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is consider ...

. Before becoming a professor at MIT, Sheffield held postdoctoral positions at

Microsoft Research Microsoft Research (MSR) is the research subsidiary of Microsoft. It was created in 1991 by Richard Rashid, Bill Gates and Nathan Myhrvold with the intent to advance state-of-the-art computing and solve difficult world problems through technologi ...

, the

University of California at Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant univ ...

, and the

. He was also an associate professor at

New York University New York University (NYU) is a private research university in New York City. Chartered in 1831 by the New York State Legislature, NYU was founded by a group of New Yorkers led by then-Secretary of the Treasury Albert Gallatin. In 1832, the ...

Awards

Scott Sheffield received the

Loève Prize The Line and Michel Loève International Prize in Probability (Loève Prize) was created in 1992 in honor of Michel Loève by his widow Line. The prize, awarded every two years, is intended to recognize outstanding contributions by researchers i ...

, the

Presidential Early Career Award for Scientists and Engineers The Presidential Early Career Award for Scientists and Engineers (PECASE) is the highest honor bestowed by the United States government on outstanding scientists and engineers in the early stages of their independent research careers. The White ...

, the

Sloan Research Fellowship The Sloan Research Fellowships are awarded annually by the Alfred P. Sloan Foundation since 1955 to "provide support and recognition to early-career scientists and scholars". This program is one of the oldest of its kind in the United States. ...

, and the

Rollo Davidson Prize The Rollo Davidson Prize is a prize awarded annually to early-career probabilists by the Rollo Davidson trustees. It is named after English mathematician Rollo Davidson (1944–1970). Rollo Davidson Trust In 1970, Rollo Davidson, a Fellow-elec ...

. He was also an invited speaker at the 2010 meeting of the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

and a plenary speaker in 2022. In 2017 he received the

Clay Research Award __NOTOC__ The Clay Research Award is an annual award given by the Oxford-based Clay Mathematics Institute to mathematicians to recognize their achievement in mathematical research. The following mathematicians have received the award: {, class=" ...

jointly with Jason Miller. He was elected to the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and ...

in 2021. In 2023 he received the Leonard Eisenbud Prize for Mathematics and Physics of the

AMS AMS or Ams may refer to: Organizations Companies * Alenia Marconi Systems * American Management Systems * AMS (Advanced Music Systems) * ams AG, semiconductor manufacturer * AMS Pictures * Auxiliary Medical Services Educational institutions * A ...

jointly with Jason Miller.

Books

*Scott Sheffield (2005), Random Surfaces, American Mathematical Society

References

{{DEFAULTSORT:Sheffield, Scott 1973 births Living people 20th-century American mathematicians 21st-century American mathematicians Harvard University alumni Probability theorists Stanford University alumni Fellows of the American Academy of Arts and Sciences