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J. Michael Boardman教授和日本京都大学西田吾郎教授为期一年的合作研究项目。研究人员将对同伦理论的最新进展进行研究。该计划的一个重点将是在光谱范畴的同调代数的最新进展及其与色程序的相互作用，但它也是一个机会来回顾该领域的最新发展作为一个整体。该计划将在学年期间主办每周研讨会，并于2000年3月举行一次会议和研讨会。这十年来，同伦理论取得了革命性的发展，本课程是一个回顾、评估和合理化这项工作的机会。环谱及其模的理论基础问题，阻碍了本学科的发展二十年，已经通过同调代数经典技术的复杂推广得到了解决。本计划的目标之一是使这些发展引起更广泛的数学界的注意。该项目汇集了两个具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，使同伦领域的研究人员了解最新的发展，从而使他们能够扩大自己研究项目的范围。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，该项目将扩大我们的基础知识基础，促进国际了解与合作。研究人员计划出版一卷，其中包含了为期一年的研讨会上提出的作品

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.***