Oded Schramm

Oded Schramm (; December 10, 1961 – September 1, 2008) was an Israeli-American mathematician known for the invention of the Schramm–Loewner evolution (SLE) and for working at the intersection of conformal field theory and probability theory.

Biography Schramm was born in Jerusalem.

On September 1, 2008, Schramm fell to his death while scrambling Guye Peak, north of Snoqualmie Pass in Washington.

Research Illustration by Schramm of an approximate conformal map using the circle packing theorem. 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 was the invention of Schramm–Loewner evolution, a tool which has paved the way for mathematical proofs of conjectured scaling limit relations on models from statistical mechanics such as self-avoiding random walk and percolation. This technique has had a profound impact on the field. was in complex analysis, 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:

The circle packing theorem 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 non-amenable 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) Salem Prize (2001) Clay Research Award (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. 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 George Pólya Prize (2006), 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. Ostrowski Prize (2007) Elected in 2008 as a foreign member of the Royal Swedish Academy of Sciences.

Selected publications . Schramm's paper introducing the Schramm–Loewner evolution.