Oded Schramm

Oded Schramm

Oded Schramm ( Hebrew עודד שרם; *  December 10, 1961 in Jerusalem ; † September 1, 2008 at Guye Peak in Washington ) was an Israeli mathematician and mathematical physicist who dealt primarily with mathematical statistical physics, combinatorics, conformal mapping and probability theory. He is known for introducing the Schramm-Löwner evolution .

Life

Schramm studied at the Hebrew University in Jerusalem, where he received his master's degree in mathematics in 1987 and then went to the United States. In 1990 he did his doctorate with William Thurston at Princeton University on (circular) packings and conformal mappings ("Packing two dimensional bodies with prescribed combinatorics and applications to the construction of conformal and quasiconformal mappings"). From 1990 to 1992 he was at the University of California, San Diego , and from 1992 to 1999 at the Weizmann Institute of Science . From 1999 he was a Senior Researcher in Mathematics at Microsoft Research in Redmond .

Schramm was a passionate mountain hiker and died in an accident while hiking on Guye Peak. He was married and had two children.

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While still pursuing topics from his doctoral thesis, he proved with Z.-X. He is the countable case of a conjecture by Paul Koebe about the conformal uniformization of multiple contiguous areas through areas delimited by circles.

Schramm introduced the method of stochastic Löwner Evolution (Stochastic Löwner Evolution, SLE, also Schramm-Löwner Evolution ). He built on the work of Charles Loewner (1893–1968) in the theory of conformal mapping. Stochastic Loewner Evolution is a one-parameter family (cluster) of paths in the complex plane with a stochastic generation rule can be described with the help of numerous stochastic geometries that are very sensitive to the value of the parameter (a kind of diffusion rate) of depend. With their help, he and others were able to show the conformal invariance and the existence of the scaling limit value of some two-dimensional grid models of statistical mechanics (at the critical point). a. at various forms of two-dimensional percolation in "loop erased random walk" (also called "uniform spanning trees") and "self Avoiding random walk" (not intersecting random walks ). In the theory of phase transitions in two-dimensional systems, conformal field theories were widely used by physicists, especially in the 1980s. With his SLE, Schramm opened up the possibility of laying the strict mathematical foundations for this. He often worked with Gregory F. Lawler and Wendelin Werner , who received the Fields Medal for work in this field . Among other things, they also proved a conjecture by Benoît Mandelbrot that the fractal dimension of the edge areas of two-dimensional Brownian motion is 4/3. ${\displaystyle \kappa }$ ${\displaystyle SLE_{\kappa }}$

Honors

Schramm received the Anna and Lajos Erdős Prize in Mathematics in 1996 , the Salem Prize in 2001 , the Clay Research Award in 2002 , the Henri Poincaré Prize and the Loève Prize in 2003, and the SIAM Polya Prize in 2006 (with Gregory Lawler and Wendelin Werner) and the Ostrowski Prize in 2007 . He gave plenary lectures at the 4th European Congress of Mathematicians 2004 ( Emergence of symmetry: conformal invariance in scaling limits of random systems ) and at the International Congress of Mathematicians 2006 in Madrid ( Conformally invariant scaling limits: an overview and a collection of problems ). According to the New York Times obituary, he would almost certainly have received the Fields Medal in 2002 for his work (like Werner in 2006) had it not been limited to mathematicians aged 40 or under. In 2008 he was elected to the Royal Swedish Academy of Sciences .

See also

• Benjamini-Schramm Convergence

Fonts

• Itai Benjamini , Olle Häggström (Ed.): Selected Works of Oded Schramm, Springer 2011
• Scaling limits of loop-erased random walks and uniform spanning trees , Israel Journal of Mathematics, Volume 118, 2000, pp. 221-288, Arxiv
• Conformally invariant scaling limits: an overview and a collection of problems , ICM 2006

Web links

• Homepage at Microsoft (English)
• Clay Research zu Schramm ( Memento from March 23, 2013 in the Internet Archive )
• Speech by Aizenman to Poincare Price (English)
• Schramm Scaling limit of loop erased random walks and uniform spanning trees , Israel Journal of Mathematics, Vol. 118, 2000, pp. 221-288 (English)
• Obituary in the New York Times (English)