Oded Schramm
Oded Schramm  

Oded Schramm


Born  Jerusalem, Israel 
December 10, 1961
Died  September 1, 2008 Washington State, USA 
(aged 46)
Citizenship  Israeli and US 
Institutions  Microsoft Research 
Doctoral advisor  William Thurston 
Doctoral students  Omer Angel 
Known for  SLE, circle packing 
Notable awards  Erdős Prize (1996) Salem Prize (2001) Clay Research Award (2002) Loève Prize (2003) Henri Poincaré Prize (2003) SIAM George Pólya Prize (2006) Ostrowski Prize (2007) 
Oded Schramm (Hebrew: עודד שרם) (December 10, 1961 – September 1, 2008) was an IsraeliAmerican mathematician known for the invention of the Schramm–Loewner evolution (SLE) and for working at the intersection of conformal field theory and probability theory.^{[1]}^{[2]}
Contents
Biography
Schramm was born in Jerusalem in Israel.^{[3]} His father, Michael Schramm, was a biochemistry professor at the Hebrew University of Jerusalem.
He attended Hebrew University where he received his bachelor’s degree in mathematics and computer science in 1986 and his master's degree in 1987, under the supervision of Gil Kalai. He then received his Ph.D. from Princeton University in 1990 under the supervision of William Thurston.
After receiving his doctorate, he worked for two years at the University of California, San Diego, and then had a permanent position at the Weizmann Institute from 1992 to 1999. In 1999 he moved to the Theory Group at Microsoft Research in Redmond, Washington, where he remained for the rest of his life.
He and his wife had two children.^{[3]}
On September 1, 2008, Schramm fell to his death while solo climbing Guye Peak, north of Snoqualmie Pass in Washington.^{[3]}^{[4]}^{[5]}
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.
Schramm's most significant contribution is the invention of Schramm–Loewner evolution, a tool which has paved the way for mathematical proofs of conjectured scaling limit relations^{[6]}^{[7]} on models from statistical mechanics such as selfavoiding random walk and percolation. This technique has had a profound impact on the field.^{[3]}^{[8]} It has been recognized by many awards to Schramm and others, including a Fields Medal to Wendelin Werner, who was one of Schramm's principal collaborators, along with Gregory Lawler. The New York Times wrote in his obituary:
“  If Dr. Schramm had been born three weeks and a day later, he would almost certainly have been one of the winners of the Fields Medal, perhaps the highest honor in mathematics, in 2002.  ” 
Schramm's doctorate ^{[9]} was in complex analysis, but he made contributions in many other areas of pure mathematics, although selftaught 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.^{[10]}
Besides conformally invariant planar processes and SLE, he made fundamental contributions to several topics:^{[8]}
 Circle packings and discrete conformal geometry.
 Embeddings of Gromov hyperbolic spaces.
 Percolation, uniform and minimal spanning trees and forests, harmonic functions on Cayley graphs of infinite finitely generated groups (especially nonamenable groups) and the hyperbolic plane.
 Limits of sequences of finite graphs.
 Noise sensitivity of Boolean functions, with applications to dynamical percolation.
 Random turn games (e.g. random turn hex) and the infinity Laplacian equation.
 Random permutations.
Awards and honors
 Erdős Prize (1996)^{[11]}
 Salem Prize (2001)^{[12]}
 Clay Research Award (2002),^{[13]} 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. ^{[13]}
 Loève Prize (2003)
 Henri Poincaré Prize (2003),^{[14]} 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.^{[15]}
 SIAM George Pólya Prize (2006),^{[16]} with Gregory Lawler and Wendelin Werner, 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. ^{[17]}
 Ostrowski Prize (2007)
 Elected in 2008 as a foreign member of the Royal Swedish Academy of Sciences.^{[18]}
Selected publications
 Schramm, Oded (2000), "Scaling limits of looperased random walks and uniform spanning trees", Israel Journal of Mathematics, 118: 221–288, arXiv:math.PR/9904022, doi:10.1007/BF02803524, MR 1776084<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>. Schramm's paper introducing the Schramm–Loewner evolution.
 Schramm, Oded (2007), "Conformally invariant scaling limits: an overview and a collection of problems", International Congress of Mathematicians. Vol. I, Eur. Math. Soc., Zürich, pp. 513–543, arXiv:math/0602151, Bibcode:2006math......2151S, ISBN 9783037190227, MR 2334202<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 Schramm, Oded (2011), Benjamini, Itai; Häggström, Olle (eds.), Selected works of Oded Schramm, Selected Works in Probability and Statistics, New York: Springer, doi:10.1007/9781441996756, ISBN 9781441996749, MR 2885266<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
References
 ↑ "Clay Mathematics Institute". Retrieved 20080912.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ Lawler, Gregory F. (2005), Conformally Invariant Processes in the Plane, Mathematical Surveys and Monographs, 114, Providence, RI: American Mathematical Society, ISBN 0821836773, MR 2129588<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ ^{3.0} ^{3.1} ^{3.2} ^{3.3} Chang, Kenneth (September 10, 2008), "Oded Schramm, 46, Mathematician, Is Dead", New York Times<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ Gutierrez, Scott (September 3, 2008), "Rescuers recover hiker's body near Cascades' Guye Peak", Seattle PostIntelligencer<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ "Accomplished Microsoft mathematician died in hiking accident", Seattle Times, September 4, 2008<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ Cardy, John (1992), "Critical percolation in finite geometries", J. Phys. A: Math. Gen., 25 (4): L201–L206, arXiv:hepth/9111026, Bibcode:1992JPhA...25L.201C, doi:10.1088/03054470/25/4/009, MR 1151081<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ Cardy, John (2002), "Crossing formulae for critical percolation in an annulus", J. Phys. A: Math. Gen., 35 (41): L565–L572, doi:10.1088/03054470/35/41/102, MR 1946958<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ ^{8.0} ^{8.1} "Oded Schramm's publications on Google Scholar".<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ Schramm, Oded (2007), Combinatorically Prescribed Packings and Applications to Conformal and Quasiconformal Maps (modified version of Schramm's Ph.D. thesis from 1990)
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(help), 0709, p. 710, arXiv:0709.0710, Bibcode:2007PhDT.......441S<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>.  ↑ "Mathematician who made a significant contribution to the study of probability and fractals", Daily Telegraph, September 19, 2008<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ The Anna and Lajos Erdős Prize in Mathematics, Technion.
 ↑ Kehoe, Elaine (2001), "Schramm and Smirnov Awarded 2001 Salem Prize" (PDF), Notices of the American Mathematical Society, 48 (8): 831<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ ^{13.0} ^{13.1} "Clay Research Award citation: Oded Schramm". Clay Mathematics Institute. Retrieved 20080904.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ "The Henri Poincaré Prize". International Association of Mathematical Physics. Retrieved 20080904.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ "Henri Poincaré Prize of the IAMP" (PDF). International Association of Mathematical Physics.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ "Gregory F. Lawler, Oded Schramm and Wendelin Werner receive George Polya Prize in Boston". Society for Industrial and Applied Mathematics. 20060420. Retrieved 20080904.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ "2006 Prizes and Awards Luncheon – SIAM Annual Meeting – July 11, 2006". SIAM.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
 ↑ "About Microsoft Research: Awards". Microsoft. Retrieved 20080912.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
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, University of California, Berkeley in May 2001.
 Conformally Invariant Scaling Limits and SLE, MSRI presentation by Oded Schramm, May 2001.
 Terence Tao, "Oded Schramm".
 Publication list
 Oded Schramm at the Mathematics Genealogy Project
 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
 O'Connor, John J.; Robertson, Edmund F., "Oded Schramm", MacTutor History of Mathematics archive, University of St Andrews<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>.
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