NSF East Asia and Pacific Summer Institute for FY 2012 in Japan

Yoshizawa Michael M, Goleta CA

Investigators

Abstract

This action funds Michael Makoto Yoshizawa of the University of California, Santa Barbara to conduct a research project, entitled "Developing a criterion for the structural complexity of a 3-dimensional space" during the summer of 2012 at Nara Women's University in Nara, Nara Prefecture, Japan. The host scientist is Professor Tsuyoshi Kobayashi. This research project aims to improve the understanding of the structure of 3-manifolds, which are spaces with the property that any inhabitants would perceive their surroundings as 3-dimensional. Thus, 3-manifolds are of interest due to their resemblance to our own universe. One tool in studying 3-manifolds is a Heegaard splitting, which is a method of decomposing a 3-manifold into two simpler pieces. Understanding properties of the Heegaard splitting, such as its distance (a measure of the splitting's complexity), can yield insight about the original 3-manifold. This research focuses on developing a new criterion to identify higher distance Heegaard splittings. Broader Impacts of an EAPSI fellowship include providing the Fellow a first-hand research experience outside the U.S.; an introduction to the science, science policy, and scientific infrastructure of the respective location; and an orientation to the society, culture and language. These activities meet the NSF goal to educate for international collaborations early in the career of its scientists, engineers, and educators, thus ensuring a globally aware U.S. scientific workforce.