Workshop on n-Categories: Foundations and Applications

University Of Chicago, Chicago IL

Investigators

Abstract

Abstract Award: DMS-0354538 Principal Investigator: J. Peter May and John C. Baez The 2004 Summer Program of the Institute for Mathematics and its Applications is on "n-Categories: Foundations and Applications," to be held in Minneapolis, Minnesota at the Institute's facilities at the University of Minnesota - Twin Cities. This award provides participant support to augment the summer program's membership and to make it possible for a group of workshop participants to join the lead organizer and his students in a post-workshop working session at the University of Chicago. The proposal describes the emerging theory of n-categories as an area of international attention but of relatively little presence in the U.S. The Institute's summer program and the subsequent working session particularly aim to expose U.S. students and junior researchers to the variety of ideas on n-categories being pursued internationally. The post-workshop working group is an attempt to focus heightened energies resulting from the workshop onto problems of greatest promise, as identified during the workshop, and is an innovation whose progress will be watched with interest. The mathematical idea of a "category" is a versatile notion defined in the mid-20th century to encapsulate the common features of a large variety of mathematical objects. Although abstract, the ideas of category theory are widely useful because they facilitate knowledge transfer from one domain to another, for example, from algebra to theoretical computer science. At the end of the 20th century several complicated notions of "n-category" had come into play to meet the needs of several areas of algebra, geometry, and physical theory, but we do not have a definition yet of "n-category" that is as broadly applicable as the original idea. The expository and research work of the leaders of this summer program aims to achieve that missing synthesis.