Oded Schramm
Oded Schramm (Hebrew עודד שרם; born December 10, 1961 in Jerusalem, † September 1, 2008 at Guye Peak in Washington) was an Israeli mathematician and mathematical physicist, and especially with mathematical statistical physics, combinatorics, conformal mappings probability theory employed.
Life
Schramm graduated from the Hebrew University in Jerusalem, where in 1987 he took his master's degree in mathematics and then went to the United States. In 1990 he received his doctorate at William Thurston at Princeton University on ( circle ) packings and conformal mappings ( "Packing two dimensional bodies with Prescribed combinatorics and applications to the construction of conformal and quasiconformal mappings "). 1992 to 1999 he was at the Weizmann Institute of Science, and at the same time from 1990 to 1992 at the University of California, San Diego. From 1999 on, he was a Senior Researcher at Microsoft Research in Mathematics in Redmond.
Schramm was a passionate hiker died in an accident during a hike on Guye Peak. He was married and had two children.
Work
Still in pursuit of topics from his doctoral thesis, he proved with Z.-X. Hey the countable case of a conjecture of Paul Koebe over the conformal uniformization multiply connected regions by limited areas of circles.
Schramm introduced the method of stochastic Loewner evolution ( Stochastic Loewner Evolution, SLE, and Schramm - Loewner Evolution ). He built on the work of Charles Loewner (1893-1968) in the theory of conformal mappings on. The stochastic Loewner evolution is a one-parameter family (cluster ) of paths in the complex plane with a stochastic production rule with the aid of numerous stochastic geometry can be described, which is very sensitive to the value of the parameter ( a kind of diffusion rate) of the dependent. With their help could from him and others, the conformal invariance and the existence of the scaling limit of some two-dimensional lattice models of statistical mechanics are shown ( at the critical point ), including in 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 of two-dimensional systems conformal field theories of physicists had been used particularly in the 1980s much. Schramm offered the possibility to lay the rigorous mathematical foundations with his SLE. Frequently he worked there with Gregory F. Lawler and Wendelin Werner, who was awarded the Fields Medal for work in this environment. Among other things, it also proved a conjecture of Benoît Mandelbrot, the fractal dimension of the border areas of two-dimensional Brownian motion 4/3 is.
Honors
Schramm received the 1996 Anna and Lajos Erdős Prize in Mathematics, 2001 Salem Prize, the 2002 Clay Research Award, in 2003 the Henri Poincaré Prize and the Loève Prize, the 2006 Polya Prize of the SIAM ( with Gregory Lawler and Wendelin Werner) and 2007 Ostrowski prize. He held 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 in Madrid in 2006 ( Conformally invariant scaling limits: an overview and a collection of problems ). According to the obituary of the New York Times, he would almost certainly for his work received the Fields Medal in 2002 ( as Werner 2006), when this would not have been limited to a mathematician not exceeding 40 years. In 2008 he was elected to the Royal Swedish Academy of Sciences.