Oded Schramm ( he, עודד שרם; December 10, 1961 – September 1, 2008) was an Israeli-American mathematician known for the invention of the

Schramm–Loewner evolution In probability theory, the Schramm–Loewner evolution with parameter ''κ'', also known as stochastic Loewner evolution (SLE''κ''), is a family of random planar curves that have been proven to be the scaling limit of a variety of two-dimensiona ...

(SLE) and for working at the intersection of

conformal field theory A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometimes ...

and

probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...

Biography

Schramm was born in

Jerusalem Jerusalem (; he, יְרוּשָׁלַיִם ; ar, القُدس ) (combining the Biblical and common usage Arabic names); grc, Ἱερουσαλήμ/Ἰεροσόλυμα, Hierousalḗm/Hierosóluma; hy, Երուսաղեմ, Erusałēm. i ...

. His father, Michael Schramm, was a biochemistry professor at the

Hebrew University of Jerusalem The Hebrew University of Jerusalem (HUJI; he, הַאוּנִיבֶרְסִיטָה הַעִבְרִית בִּירוּשָׁלַיִם) is a public research university based in Jerusalem, Israel. Co-founded by Albert Einstein and Dr. Chaim Weiz ...

. He attended Hebrew University, where he received his

bachelor's degree A bachelor's degree (from Middle Latin ''baccalaureus'') or baccalaureate (from Modern Latin ''baccalaureatus'') is an undergraduate academic degree awarded by colleges and universities upon completion of a course of study lasting three to six ...

in mathematics and computer science in 1986 and his master's degree in 1987, under the supervision of

Gil Kalai Gil Kalai (born 1955) is the Henry and Manya Noskwith Professor Emeritus of Mathematics at the Hebrew University of Jerusalem, Israel, Professor of Computer Science at the Interdisciplinary Center, Herzliya, and adjunct Professor of mathematics a ...

. He then received his PhD from

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

in 1990 under the supervision of

William Thurston William Paul Thurston (October 30, 1946August 21, 2012) was an American mathematician. He was a pioneer in the field of low-dimensional topology and was awarded the Fields Medal in 1982 for his contributions to the study of 3-manifolds. Thurston ...

. After receiving his doctorate, he worked for two years at the

University of California, San Diego The University of California, San Diego (UC San Diego or colloquially, UCSD) is a public university, public Land-grant university, land-grant research university in San Diego, California. Established in 1960 near the pre-existing Scripps Insti ...

, and then had a permanent position at the

Weizmann Institute The Weizmann Institute of Science ( he, מכון ויצמן למדע ''Machon Vaitzman LeMada'') is a public research university in Rehovot, Israel, established in 1934, 14 years before the State of Israel. It differs from other Israeli univ ...

from 1992 to 1999. In 1999 he moved to the Theory Group 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 ...

Redmond, Washington Redmond is a city in King County, Washington, United States, located east of Seattle. The population was 73,256 at the 2020 census, up from 54,144 in 2010. Redmond is best known as the home of Microsoft and Nintendo of America. With an an ...

, where he remained for the rest of his life. He and his wife had two children, Tselil and Pele. Tselil is an assistant professor of statistics at Stanford University. On September 1, 2008, Schramm fell to his death while

scrambling Scrambling is a mountaineering term for ascending steep terrain using one's hands to assist in holds and balance.''New Oxford American Dictionary''. It is also used to describe terrain that falls between hiking and rock climbing (as a “scramb ...

Guye Peak Guye Peak is a mountain in the northwest United States in the Cascade Range of Washington, east of Seattle. Named for Francis M. Guye, who held an iron mining claim on it in the 1880s, it lies in the Alpine Lakes Wilderness area and overlooks S ...

, north of

Snoqualmie Pass Snoqualmie Pass is a mountain pass that carries Interstate 90 (I-90) through the Cascade Range in the U.S. state of Washington. The pass summit is at an elevation of , on the county line between Kittitas County and King County. Snoqualmie Pass ...

Washington Washington commonly refers to: * Washington (state), United States * Washington, D.C., the capital of the United States ** A metonym for the federal government of the United States ** Washington metropolitan area, the metropolitan area centered on ...

Research

A constant theme in Schramm's research was the exploration of relations between discrete models and their continuous scaling limits, which for a number of models turn out to be

conformally invariant In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed versio ...

. Schramm's most significant contribution was the invention of

, a tool which has paved the way for mathematical proofs of conjectured scaling limit relations on models from

statistical mechanics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic be ...

such as self-avoiding random walk and

percolation Percolation (from Latin ''percolare'', "to filter" or "trickle through"), in physics, chemistry and materials science, refers to the movement and filtering of fluids through porous materials. It is described by Darcy's law. Broader applicatio ...

. This technique has had a profound impact on the field. It has been recognized by many awards to Schramm and others, including a

Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award ho ...

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 ...

, who was one of Schramm's principal collaborators, along with Gregory Lawler. ''

The New York Times ''The New York Times'' (''the Times'', ''NYT'', or the Gray Lady) is a daily newspaper based in New York City with a worldwide readership reported in 2020 to comprise a declining 840,000 paid print subscribers, and a growing 6 million paid ...

'' wrote in his obituary: Schramm's doctorate. Modified version of Schramm's Ph.D. thesis from 1990. was in

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates Function (mathematics), functions of complex numbers. It is helpful in many branches of mathemati ...

, but he made contributions in many other areas of pure mathematics, although self-taught in those areas. Frequently he would prove a result by himself before reading the literature to obtain an appropriate credit. Often his proof was original or more elegant than the original. Besides conformally invariant planar processes and SLE, he made fundamental contributions to several topics: *

Circle packing In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that no circle can be enlarged without creating an overlap. The associated ''packing den ...

s and discrete

conformal geometry In mathematics, conformal geometry is the study of the set of angle-preserving ( conformal) transformations on a space. In a real two dimensional space, conformal geometry is precisely the geometry of Riemann surfaces. In space higher than two d ...

. * Embeddings of

Gromov hyperbolic space In mathematics, a hyperbolic metric space is a metric space satisfying certain metric relations (depending quantitatively on a nonnegative real number δ) between points. The definition, introduced by Mikhael Gromov, generalizes the metric properti ...

s. *

Percolation Percolation (from Latin ''percolare'', "to filter" or "trickle through"), in physics, chemistry and materials science, refers to the movement and filtering of fluids through porous materials. It is described by Darcy's law. Broader applicatio ...

uniform A uniform is a variety of clothing worn by members of an organization while participating in that organization's activity. Modern uniforms are most often worn by armed forces and paramilitary organizations such as police, emergency services, se ...

and minimal spanning trees and forests,

harmonic function In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f: U \to \mathbb R, where is an open subset of that satisfies Laplace's equation, that is, : \f ...

s on

Cayley graph In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group is a graph that encodes the abstract structure of a group. Its definition is suggested by Cayley's theorem (named after Arthur Cayle ...

s of infinite finitely generated groups (especially non-amenable groups) and the

hyperbolic plane In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai– Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: :For any given line ''R'' and point ''P'' ...

. * Limits of sequences of finite

graphs Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discre ...

. * Noise sensitivity of

Boolean function In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually , or ). Alternative names are switching function, used especially in older computer science literature, and truth function ( ...

s, with applications to dynamical percolation. * Random turn games (e.g. random turn hex) and the

infinity Laplacian In mathematics, the infinity Laplace (or L^\infty-Laplace) operator is a 2nd-order partial differential operator, commonly abbreviated \Delta_\infty. It is alternately defined by :\Delta_\infty u(x) = \langle Du, D^2 u \, Du \rangle = \sum_ \frac ...

equation. *

Random permutation A random permutation is a random ordering of a set of objects, that is, a permutation-valued random variable. The use of random permutations is often fundamental to fields that use randomized algorithms such as coding theory, cryptography, and sim ...

Awards and honors

Erdős Prize The Anna and Lajos Erdős Prize in Mathematics is a prize given by the Israel Mathematical Union to an Israeli mathematician (in any field of mathematics and computer science), "with preference to candidates up to the age of 40." The prize was e ...

(1996) *

Salem Prize The Salem Prize, in memory of Raphael Salem, is awarded each year to young researchers for outstanding contributions to the field of analysis. It is awarded by the School of Mathematics at the Institute for Advanced Study in Princeton and was fo ...

(2001) *

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=" ...

(2002), for his ''work in combining analytic power with geometric insight in the field of random walks, percolation, and probability theory in general, especially for formulating stochastic Loewner evolution. His work opens new doors and reinvigorates research in these fields.'' *

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 ...

(2003) *

Henri Poincaré Prize The Henri Poincaré Prize is awarded every three years since 1997 for exceptional achievements in mathematical physics and foundational contributions leading to new developments in the field. The prize is sponsored by the Daniel Iagolnitzer Foundat ...

(2003), ''For his contributions to discrete conformal geometry, where he discovered new classes of circle patterns described by integrable systems and proved the ultimate results on convergence to the corresponding conformal mappings, and for the discovery of the Stochastic Loewner Process as a candidate for scaling limits in two dimensional statistical mechanics.'' *

SIAM Thailand ( ), historically known as Siam () and officially the Kingdom of Thailand, is a country in Southeast Asia, located at the centre of the Mainland Southeast Asia, Indochinese Peninsula, spanning , with a population of almost 70 mi ...

George Pólya Prize The Society for Industrial and Applied Mathematics (SIAM) has three prizes named after George Pólya: the George Pólya Prize for Mathematical Exposition, established in 2013; the George Pólya Prize in Applied Combinatorics, established in 1969 ...

(2006), with Gregory Lawler and

, for ''groundbreaking work on the development and application of stochastic Loewner evolution (SLE). Of particular note is the rigorous establishment of the existence and conformal invariance of critical scaling limits of a number of 2D lattice models arising in statistical physics.'' *

Ostrowski Prize The Ostrowski Prize is a mathematics award given every odd year for outstanding mathematical achievement judged by an international jury from the universities of Basel, Jerusalem, Waterloo and the academies of Denmark and the Netherlands. Alexand ...

(2007) * Elected in 2008 as a foreign member of the

Royal Swedish Academy of Sciences The Royal Swedish Academy of Sciences ( sv, Kungliga Vetenskapsakademien) is one of the Swedish Royal Academies, royal academies of Sweden. Founded on 2 June 1739, it is an independent, non-governmental scientific organization that takes special ...

Selected publications

*. Schramm's paper introducing the

. * *

References

External links

Tutorial: SLE
video of MSRI lecture given jointly by Schramm, Lawler and Werner in the special session at the

Lawrence Hall of Science The Lawrence Hall of Science is a public science center in Berkeley, California that offers hands-on science exhibits, designs curriculum, aids professional development, and offers after school science resources to students of all ages. The Hall ...

University of California, 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 u ...

in May 2001.
Conformally Invariant Scaling Limits and SLE
MSRI presentation by Oded Schramm, May 2001. *

Terence Tao Terence Chi-Shen Tao (; born 17 July 1975) is an Australian-American mathematician. He is a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins chair. His research includes ...

"Oded Schramm"

*
Oded Schramm Memorial page

Oded Schramm Memorial blog

Oded Schramm Memorial Workshop – August 30–31, 2009 at Microsoft Research

Oded Schramm obituary in the IMS Bulletin
* {{DEFAULTSORT:Schramm, Oded 1961 births 2008 deaths Probability theorists 20th-century Israeli mathematicians 20th-century American mathematicians 21st-century American mathematicians Princeton University alumni Mountaineering deaths Sports deaths in Washington (state) Members of the Royal Swedish Academy of Sciences People from Redmond, Washington Hebrew University of Jerusalem alumni Weizmann Institute of Science faculty Clay Research Award recipients Scientists from Jerusalem Erdős Prize recipients