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.

2006 Research Program: "Low Dimensional Topology "
Organizers:Tomasz Mrowka, Massachusetts Institute of Technology and Peter Ozsvath, Columbia University

Participants will be given the opportunity to discuss their work in a leisurely environment. There will be plenty of time for questions and comments. The goal will be to discuss current research in Low Dimensional Topology and its applications, as well as open problems and new directions.

Topics for workshops and working groups will be chosen at the beginning of the Summer Session by participants. It is expected that researchers will be active in other aspects of the PCMI Summer Session by offering talks or seminars to the other groups, or attending their sessions. The rest of the time will be free for work and informal discussions.

New and recent PhD's are especially encouraged to apply to the Research Program if they are working in this field, or a related field. Senior mathematicians whose research interests are complementary to the main topic are also invited to apply. In addition, there will be openings for senior mathematicians who wish to attend the Summer Session because of their strong interest and involvement in educational issues.

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.

• Research Program Participants

The Research Program is supported by the National Science Foundation grant no. 0437137.

The Clay Mathematics Institute Senior Scholars for PCMI 2006 are Yakov Eliashberg, Stanford University, and Robion Kirby, University of California Berkeley.