This award supports a one year collaborative research project between Professor J. Michael Boardman of Johns Hopkins University in Baltimore and Professor Goro Nishida of Kyoto University in Japan. The researchers will be undertaking a study of the recent progress is homotopy theory. One focus of the program will be recent advances in homological algebra in the category of spectra and their interaction with the chromatic program, but it is also an opportunity to review recent developments in the field as a whole. The program will sponsor weekly seminars during the academic year, culminating in a conference and workshop in March, 2000. This decade has seen revolutionary developments in homotopy theory, and this program is an opportunity to review, evaluate, and rationalize this work. Problems with the foundations of the theory of ring-spectra and their modules, which have blocked the development of the subject for two decades, have been solved by sophisticated generalizations of classical techniques from homological algebra. A goal of this program is to bring these developments to the attention of the wider mathematical community.
This project brings together the efforts of two laboratories that have complementary expertise and research capabilities. Results of this research would provide a forum for informing researchers, in the area of homotopy, of the latest developments and, therefore, enabling them to expand the scope of their own research projects. This research advances international human resources through the participation of a younger scientist and graduate students. Through the exchange of ideas and technology, this project will broaden our base of basic knowledge and promote international understanding and cooperation. The researchers plan to publish a volume that contains the works presented in the year-long seminar. ***
