U.S.-Japan Joint Seminar: Quantum Geometry in Dimensions 2 and 4

Johns Hopkins University, Baltimore MD

Investigators

Abstract

0089657 Morava This award supports the participation of American scientists in a U.S.-Japan seminar on quantum geometry in dimensions 2 and 4, to be held at the Johns Hopkins University in Baltimore from March 18-24, 2002. The co-organizers are professors Jack Morava of the Johns Hopkins University and Professor Shigeyuki Morita of the Tokyo University in Japan. These are two of the most vital and rapidly developing subjects in mathematics. Mathematical physicists are conscious of deep similarities between two and four-dimensional quantum field theories, but although mathematical research in two and four-dimensional geometry has been strongly affected by ideas from physics, these fields have separate roots and separate histories. In dimension two, classification is easy, and research is concerned with families of objects. In dimension four classification is difficult, and the construction of new tools to study that topic is very active. For historical reasons, research on (families of) two-manifolds has been dominated by ideas from algebraic geometry; but while ideas from the theory of algebraic surfaces have had great impact in four-mainfold theory, the deeper developments there have been based on techniques from nonlinear analysis and gauge theory. The population of researchers interested in these subjects is thus sociologically very diverse. However, the two fields share common foundations in topology, and by keeping these fundamental issues in focus, the organizers hope for a broadly accessible program of deep interest. Seminar organizers have made a special effort to involve younger researchers and graduate students as both participants and observers. The exchange of ideas and data with Japanese experts in this field will enable U.S. participants to advance their own work, and will set the stage for future collaborative projects. Dissemination of information on the seminar will be available on the World Wide Web.