This project is to support US participant traveling to an interdisciplinary conference, "Physics-Mathematics Summer Institute (PhyMSI)", which is devoted to double affine Hecke algebras, the Langlands program, affine flag varieties, conformal field theory, super Yang-Mills theory and the AdS-CFT correspondence. It will be held in June-July 2011 (Cargese, Luminy). The conference consists of two major components: The Langlands program and double affine Heckealgebras component contains the topics (a) Affine and double affine Hecke algebras and relations to integrable models, (b) Geometric Langlands program and the theory of affine flag varieties, and (c) Finite characteristic and the p-adic Langlands program. The emphasis is on the geometric aspects of Langlands Program and Double Affine Hecke Algebras. The super Yang Mills theory and Ads conformal field theory component are core directions of modern theoretical physics containing the main topics (a) Super Yang-Mills theory, including applications to the Langlands program, (b) AdS-CFT correspondence and integrability, (c) Conformal and superconformal field theory in diverse dimensions, and (d) New relations with algebra and geometry. The main objective of the conference is to gather leading and young researchers together and to provide an opportunity for: (a) understanding the perspectives in these highly interdisciplinary directions; (b) accelerating the progress and finding new lines of development and cooperation; (c) greater involvement of the scientists from the other fields.
The areas of Langlands program, affine flag varieties, affine Hecke algebras, double affine Hecke algebras, super Yang Mills theory and Conformal field theory are among the most active areas of current research in mathematics and physics. They are so deeply interconnected that experts in one of these fields need to constantly monitor progress in the others. This conference program will provide an opportunity for researchers working in different research areas to gather together and discuss new ideas and further interconnections among these topics. Large portion of the support will be for junior US researcher to participant in this conference and ensure that future researchers will continue be involved in the research fields and their new developments.
Interaction between physics and mathematics is vital for development of both subjects. In particular, representation theory which is the study of algebraic structure of symmetries, has its roots in quantum physic; new connections between these two subjects, as well as with algebraic geometry, have emerged in the last decade. The goal of the summer institute was to bring together researchers working in these areas in order to promote exchange of ideas and induce further progress. The conference was recognized by all participants as an outstanding interdisciplinary event that is expected to have lasting effect in mathematics and physics. The conference greatly stimulated finding new directions of research and cooperation. It attracted about 140 leading specialists in these and neighboring fields including many junior investigators; 52 participants (38%) from the USA, 38 (28%) from France, 9(7%) from Canada as well experts from 10 other countries. About 39.5% of the NSF award was used to cover expenses of junior investigators. From the 78 speakers of the conference, 6 were women. Among 78 speakers of the conference, 2 spoke twice, Edward Witten and Andrei Okounkov, and 20 speakers were junior investigators, which is a significant number for such high-profile conference. The participants appreciated the design, the scientific quality of the conference, focused and diverse exposition of the topics and the general organization of the meeting. The webpage www.mathphyz.info/ was important for success of the conference; esp. the overview mathphyz.info/overview.html, which contains a brief scientific description of the topics of the conference and related directions.
