Various recent developments in different areas of mathematics and physics turn out to be related when the language of tensor categories is used as a unifying concept. Tensor categories emerge naturally whenever a mathematical problem needs an efficient treatment of one or several products," or when a problem in theoretical physics requires a concise description of possible couplings. As a consequence, tensor categories provide a natural unifying language for many interesting problems. Using this framework has the additional benefit of unraveling structural parallels and therefore often allows one to apply results and techniques to a given problem that were originally developed in a different context.
The PI is a co-organizer of a program, Tensor Categories in Mathematics and Physics, to take place in the spring and early summer of 2004 at the Erwin Schroedinger Institute in Vienna. The purpose of this program to bring together researchers working on different topics in mathematics (such as quantum groups, link invariants, vertex algebras, or subfactors) and physics (such as topological and conformal field theory, string theory, or operator algebraic approaches to quantum theory) in which tensor categories are playing a role, or can be expected to play a role in the future.
The contribution from NSF will be primarily used to support graduate students, junior faculty, women and members of underrepresented minority groups in the United States to attend the program. Active participation in such a program will undoubtedly have an important impact on their future careers. The idea of the program is to encourage interaction between mathematicians and mathematical physicists of different backgrounds. In particular, one of the main goals of the program is to make a wealth of mathematical results and concepts that are ready to use accessible to a larger part of the theoretical physics community. It is clear that mathematicians and physicists can all benefit from communicating results between the various disciplines and from developing a unified language.
