Brownian Motion and Differential Geometry

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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.