This PIRE project involves international research and education collaboration in overlapping areas of probability theory and statistical physics: disordered systems, percolation, and Schramm-Loewner evolutions (SLEs). Participating institutions include the Courant Institute of Mathematical Sciences of New York University, the Instituto Nacional de Matemática Pura e Aplicada of Rio de Janeiro, and the Centrum voor Wiskunde en Informatica of Amsterdam. Faculty, postdocs and students from other scientific institutions are also involved in the networks and activities (such as summer and winter schools) of this PIRE project.
The project concerns random spatial processes, including disordered systems such as spin glasses and random walks with traps and in random environments, in which macroscopic phenomena are naturally expressed in terms of paths of microscopic events that percolate through space (or space-time). Scaling concepts and methods play an important role in the analysis of such processes and in the nature of their phase transitions and critical behavior. The PI, co-PIs and key international collaborators have been prime participants in some of the major progress in recent years on percolation and its scaling limits, as well as on spin glasses and disordered random walks. Among the issues addressed in this project are analyses of the percolation signature of the spin glass transition in realistic (i.e., short-range) models and of scaling limits for near-critical percolation and disordered random walks in two and more dimensions. These and related challenging problems are ripe for a collaborative attack combining the diverse expertise of the participants from the U.S. and abroad. Moreover, the new techniques being developed in this project for percolative and disordered systems can be applied in a variety of fields, including communication, materials science, neural science, theoretical computer science and petroleum engineering.
This project focuses on training U.S. students, postdoctoral fellows and faculty from various backgrounds in international education and research collaboration. PIRE postdoctoral and predoctoral fellows are expected to spend at least one semester abroad with collaborative joint mentoring by one of the international collaborators together with a Courant faculty member. Other students and postdocs will be encouraged to collaborate internationally via shorter visits and by participating in seasonal schools. A yearly winter (in the Northern hemisphere) school in Latin America starts January, 2008 in Santiago, Chile; a yearly summer school in Europe starts June, 2008 at the NYU campus in Florence, Italy.
A major goal of this project is to create an institutional basis for a self-sustaining model of enhanced collaboration at faculty, postdoctoral and student levels between the U.S., Latin America and Europe. Contacts are being made for support from foundations and industry to turn the experience developed from this PIRE project into a self-sustaining model for international collaboration in education and research. This PIRE project is funded by the Office of International Science and Engineering (OISE) with co-funding from the Division of Mathematical Sciences (DMS).
