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Random Shapes

March 12 - June 15, 2007

Program Poster PDF

Hotel Accommodation and Air Travel


Organizing Committee

Igor Frenkel (Yale University, Mathematics)
Peter Jones (Yale University, Mathematics)
Richard Kenyon (University of British Columbia, Mathematics)
Stanley Osher (IPAM, Mathematics)
Nicholas Read (Yale University, Physics)
Steffen Rohde (University of Washington, Mathematics)
Bernard Sapoval (École Polytechnique, Physics)
Leon Takhtajan (SUNY Stony Brook, Mathematics)

Scientific Background

The study of random shapes started over 100 years ago as a collection of examples, e.g. those arising from Brownian Motion. It has turned out to be a meeting place for probability theory, mathematics, physics, combinatorics, computer science, and certain areas of algebra. Recent advances in areas diverse as brain imaging, astrophysics, nanotechnology, and communications and sensor networks have been driven by notions related to random shapes or motions, and random transport. The past decade has seen both an explosion of results as well as new structures (for example, O. Schramm's SLE processes) that unify various problems. While much progress has been made, this is still a very young field. For example, one is lacking a theory similar to SLE for generating random surfaces. The purpose of this program is to bring together experts from these rapidly developing areas in mathematics and the sciences to share new ideas and study new problems. We are mainly concerned with structures in two or three dimensions, as they have a strong connection to biology and physics, but some of the topics to be covered concern higher dimensional Euclidean spaces and some problems with networks may have no specified ambient dimension. Besides these general areas, there will also be activity in the study of random shapes and complex geometries arising in brain mapping and astrophysics. The topics to be covered include:

Brownian and fractional Brownian Motion; SLE and related Löwner evolution; geometry of the Gaussian free field; self-avoiding random walk; percolation; random shapes and Wiener space in representation theory; random curves, surfaces, and growth processes; random minimal surfaces; random conformal or quasiconformal mappings; random Teichmüller theory and univalent dynamics; random welding maps; random triangulations and metrics on surfaces; 3D image processing for complex geometries; PDE’s related to growth processes.

Random curves and surfaces in conformal field theory, quantum gravity, and string theory; simulations of random curves and surfaces; folding, shrinking, wrinkling, and buckling of surfaces and membranes; random folding of polymers; geometry of random fields; electrodeposition and rough boundaries in electrochemistry; diffusion limited aggregation; branching structures and random transport; large scale cosmic fields and structures; random structures and diffusion in nanotechnology.

Computer Science
Random trees, circuits, graphs, branching processes, and related algorithms; random partitions and metrics; random polytopes; random routing and transport; random search algorithms; dynamic networks, graphs, and spanners; complex geometries in communication and sensor networks; 3D graphics for complex surfaces; computational geometry for random surfaces and sets.


This long-term program will involve a community of senior and junior researchers. The intent is for long-term participants to have an opportunity to learn about random shapes from the perspective of a variety of fields--mathematics, physics and computer science--and to meet a diverse group of people and have an opportunity to form new collaborations. In addition to these activities, there will be opening tutorials, four workshops, and a culminating workshop at Lake Arrowhead.

Full and partial support for long-term participants is available, and those interested are encouraged to fill out an online application at the bottom of this page. Support for individual workshops will also be available, and may be applied for through the online application for each workshop. We are especially interested in applicants who are interested in becoming core participants and participating in the entire program (March 12 - June 15, 2007), but give consideration to applications for shorter periods. Funding for participants is available at all academic levels, though recent PhD's, graduate students, and researchers in the early stages of their career are especially encouraged to apply.

Encouraging the careers of women and minority mathematicians and scientists is an important component of IPAM's mission and we welcome their applications.


There will be an active program of research activities, seminars and workshops throughout the March 12 - June 15, 2007 period and core participants will be in residence at IPAM continuously for these fourteen weeks. The program will open with tutorials, and will be punctuated by four major workshops and a culminating workshop at UCLA’s Lake Arrowhead Conference Center. Several distinguished senior researchers will be in residence for the entire period. Between the workshops there will be a program of activities involving the long-term and short-term participants, as well as visitors.


Contact Us:

Institute for Pure and Applied Mathematics (IPAM)
Attn: RS2007
460 Portola Plaza
Los Angeles CA 90095-7121
Phone: 310 825-4755
Fax: 310 825-4756
Email: ipam@ucla.edu
Website: http://www.ipam.ucla.edu/programs/rs2007/

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