Brownian Motion and Differential Geometry

布朗运动与微分几何 该奖项的建议是根据美国-工业化 国家科学家交流计划， 工程师，1987/1988年。 该计划旨在使 美国科学家和工程师将在研究中心进行长期研究 西欧工业化国家的教育机构 如日本、澳大利亚和新西兰。 交换奖励提供 开展联合研究和利用 独特或互补的设施，专业知识和实验 国外的条件。 奖项是根据与以下方面有关的科学标准选出的： 他/她的科学领域，申请人的未来潜力 专业成长，以及与进一步发展有关的标准 科学和工程的国际合作。 程序 特别是针对那些正在从事 他们的研究生涯。 本研究计画将随机过程应用于 微分几何中的问题 讨论的第一个领域是 利用布朗运动证明调和形式的消失定理 在完整的流形，如在早期的工作K。D.埃尔沃西和 提议者 第二个领域是使用布朗运动技术， 证明了非紧流形上的指数定理。 该项目是在史蒂芬罗森伯格博士的指导下，部门 波士顿大学，波士顿，MA 02215，美国，和 K教授D. Elworthy，数学研究所，沃里克大学， 英国考文垂CV 4 7AL 这项授标建议提供资金，酌情支付 国际旅行、当地出国旅行、津贴、家属 津贴，如果适用，语言培训，如果需要，和一个公寓 美国本土机构的行政津贴为250美元。

Brownian Motion and Differential Geometry: This award recommendation is made under the U.S.-Industrialized Countries program for the Exchange of Scientists and Engineers, 1987/1988 Competition. The program is designed to enable U.S. scientists and engineers to conduct long-term research at research institutions in the industrialized countries of Western Europe as well as Japan, Australia and New Zealand. Exchange awards provide opportunities for the conduct of joint research and the utilization of unique or complementary facilities, expertise and experimental conditions in foreign countries. Awards are selected on the basis of scientific criteria relevant to his/her field of science, the prospective potential of the applicants for professional growth, as well as criteria relevant to the furthering of international cooperation in science and engineering. The program is particularly directed to scientists and engineers who are embarking on their research careers. This research project addresses applications of stochastic processes to problems in differential geometry. The first area of discussion is the use of Brownian motion to prove vanishing theorems for harmonic forms on complete manifolds, as in earlier work of K. D. Elworthy and the proposer. The second area is the use of Brownian motion techniques to prove index theorems on noncompact manifolds. The project is under the direction of Dr. Steven Rosenberg, Department of Mathematics, Boston University, Boston, MA 02215, U.S.A., and Professor K. D. Elworthy, Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom. This award recommendation provides funds to cover, as appropriate, international travel, local travel abroad, stipend, dependents allowance, if applicable, language training, if required, and a flat administrative allowance of $250 for the U.S. home institution.