Until recently a lack of precision around China's economic size was taken for granted but caused little lost sleep: room to expand and the pace of growth were self-evident, and everything beyond that was academic for most purposes. But today the pace and even direction of China's growth is prone to volatility, and the nation is sizable enough to cause global disruption. This study reassesses China's nominal economic size from the bottom up. It compares China's practices with international standards and reviews the long-standing arguments about Chinese economic statistics to separate real...

This is a book on symplectic topology, a rapidly developing field of mathematics which originated as a geometric tool for problems of classical mechanics. Since the 1980s, powerful methods such as Gromov's pseudo-holomorphic curves and Morse-Floer theory on loop spaces gave rise to the discovery of unexpected symplectic phenomena. The present book focuses on function spaces associated with a symplectic manifold. A number of recent advances show that these spaces exhibit intriguing properties and structures, giving rise to an alternative intuition and new tools in symplectic topology. The book...

The theory of persistence modules originated in topological data analysis and became an active area of research in algebraic topology. This book provides a concise and self-contained introduction to persistence modules and focuses on their interactions with pure mathematics, bringing the reader to the cutting edge of current research. In particular, the authors present applications of persistence to symplectic topology, including the geometry of symplectomorphism groups and embedding problems. Furthermore, they discuss topological function theory, which provides new insight into oscillation...