Complementing the highly structured Graduate Summer School, which is directed at younger mathematicians, the Research Program in Mathematics addresses the needs of mathematicians who are already carrying out research. The program offers advanced scholars the opportunity to do research, collaborate with their peers, meet outstanding students, and explore new teaching ideas with professional educators. It is designed to introduce active areas of research by focusing on a specific topic. The informal format generates lively exchanges of views and information between established and newer researchers.

2007 Research Program in Statistical Mechanics

Organizers: Scott Sheffield, Courant Institute and Thomas Spencer, Institute for Advanced Study

This program will focus on recent mathematical developments in statistical mechanics as well as on new directions suggested by theoretical physics.  In addition to the topics covered by the graduate lectures, the research program will explore other active areas of mathematical physics and probability. These include the relation of conformal field theory to the Stochastic Lowner equation, nonequilibrium statistical mechanics, phase transitions, universality of critical phenomena, and supersymmetric field theories with application to polymers and branched polymers and random matrices.  Some lectures on these topics will be accessible to advanced graduate students and postdocs and while others will be intended for more specialized working groups.

A primary goal of the research program is to foster the collaboration of a diverse group of participants. At the beginning of the summer the participants will be encouraged to organize working groups.  There will be plenty of time for work and informal discussions. A related goal of this program is to highlight the relation of statistical mechanics to other parts of mathematics such as combinatorics, representation theory and geometry.

New and recent PhDs are especially encouraged to apply if they are working in probability or statistical mechanics and related fields.

Independent Researchers

Researchers in other areas of mathematics who have independent funding are invited to apply for participation in the PCMI Summer Session. All programs and facilities will be available to these participants, although lodging space may be limited. Introductory courses, joint education/research activities, and computer facilities may be of particular interest. Researchers interested in becoming involved with a future Summer Session may wish to use this opportunity to get acquainted with the program. Small groups of collaborators from geographically separate areas are particularly welcome to apply.

The Research Program is supported by the National Science Foundation grant # DMS-0437137.

The Clay Mathematics Institute Senior Scholars in Residence for PCMI 2007 are Andrei Okounkov, Princeton University and Srinivasa Varadhan, Courant Institute; support provided by the Clay Mathematics Institute..