U.S.-Japan Cooperative Science: Recent Progress in Homotopy Theory

该奖项支持巴尔的摩约翰·霍普金斯大学的J.Michael Boardman教授和日本京都大学的西田五郎教授之间为期一年的合作研究项目。研究人员将承担研究的最新进展是同伦理论。该计划的一个重点将是同调代数在光谱类别中的最新进展及其与色度计划的相互作用，但它也是一个机会来回顾整个领域的最新发展。该计划将在本学年每周举办一次研讨会，最终在2000年3月举行一次会议和研讨会。这十年见证了同伦理论的革命性发展，这个项目是一个回顾、评估和合理化这项工作的机会。环谱及其模理论的基础问题，二十年来一直阻碍着这门学科的发展，已经通过从同调代数中对经典技术的复杂推广而得到解决。这个项目的一个目标是使这些发展引起更广泛的数学界的注意。该项目汇集了两个拥有互补专业知识和研究能力的实验室的努力。这项研究的结果将提供一个论坛，向同伦领域的研究人员通报最新发展，从而使他们能够扩大自己的研究项目的范围。这项研究通过年轻科学家和研究生的参与促进了国际人力资源的发展。通过思想和技术的交流，这个项目将扩大我们的基础知识基础，促进国际理解与合作。研究人员计划出版一本包含在为期一年的研讨会上展示的作品的卷。*

9815343BoardmanThis 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.***