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Homotopy Theory: Tools and Applications
This volume contains the proceedings of the conference Homotopy Theory: Tools and Applications, in honor of Paul Goerss's 60th birthday, held from July 17–21, 2017, at the University of Illinois at Urbana-Champaign, Urbana, IL. The articles cover a variety of topics spanning the current research frontier of homotopy theory. This includes articles concerning both computations and the formal theory of chromatic homotopy, different aspects of equivariant homotopy theory and K-theory, as well as articles concerned with structured ring spectra, cyclotomic spectra associated to perfectoid fields, and the theory of higher homotopy operations.
Eulerian Spaces
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Culture and Power in the Reconstitution of the Chinese Realm, 200–600
The period between the fall of the Han in 220 and the reunification of the Chinese realm in the late sixth century receives short shrift in most accounts of Chinese history. The period is usually characterized as one of disorder and dislocation, ethnic strife, and bloody court struggles. Its lone achievement, according to many accounts, is the introduction of Buddhism. In the eight essays of Culture and Power in the Reconstitution of the Chinese Realm, 200-600, the authors seek to chart the actual changes occurring in this period of disunion, and to show its relationship to what preceded and followed it. This exploration of a neglected period in Chinese history addresses such diverse subjects as the era's economy, Daoism, Buddhist art, civil service examinations, forays into literary theory, and responses to its own history.
Traces of Grand Peace
Since the second century BC the Confucian Classics, endorsed by the successive ruling houses of imperial China, had stood in tension with the statist ideals of “big government.” In Northern Song China (960–1127), a group of reform-minded statesmen and thinkers sought to remove the tension between the two by revisiting the highly controversial classic, the Rituals of Zhou: the administrative blueprint of an archaic bureaucratic state with the six ministries of some 370 offices staffed by close to 94,000 men. With their revisionist approaches, they reinvented it as the constitution of state activism. Most importantly, the reform-councilor Wang Anshi’s (1021–1086) new commentary on the Rituals of Zhou rose to preeminence during the New Policies period (ca. 1068–1125), only to be swept into the dustbin of history afterward. By reconstructing his revisionist exegesis from its partial remains, this book illuminates the interplay between classics, thinkers, and government in statist reform, and explains why the uneasy marriage between classics and state activism had to fail in imperial China.
Stable Stems
The author presents a detailed analysis of 2-complete stable homotopy groups, both in the classical context and in the motivic context over C. He uses the motivic May spectral sequence to compute the cohomology of the motivic Steenrod algebra over C through the 70-stem. He then uses the motivic Adams spectral sequence to obtain motivic stable homotopy groups through the 59-stem. He also describes the complete calculation to the 65-stem, but defers the proofs in this range to forthcoming publications. In addition to finding all Adams differentials, the author also resolves all hidden extensions by 2, η, and ν through the 59-stem, except for a few carefully enumerated exceptions that remain ...
The Adams Spectral Sequence for Topological Modular Forms
The connective topological modular forms spectrum, tmf, is in a sense initial among elliptic spectra, and as such is an important link between the homotopy groups of spheres and modular forms. A primary goal of this volume is to give a complete account, with full proofs, of the homotopy of tmf and several tmf-module spectra by means of the classical Adams spectral sequence, thus verifying, correcting, and extending existing approaches. In the process, folklore results are made precise and generalized. Anderson and Brown-Comenetz duality, and the corresponding dualities in homotopy groups, are carefully proved. The volume also includes an account of the homotopy groups of spheres through degr...
Algebraic Topology: Applications and New Directions
This volume contains the proceedings of the Stanford Symposium on Algebraic Topology: Applications and New Directions, held from July 23-27, 2012, at Stanford University, Stanford, California. The symposium was held in honor of Gunnar Carlsson, Ralph Cohen and Ib Madsen, who celebrated their 60th and 70th birthdays that year. It showcased current research in Algebraic Topology reflecting the celebrants' broad interests and profound influence on the subject. The topics varied broadly from stable equivariant homotopy theory to persistent homology and application in data analysis, covering topological aspects of quantum physics such as string topology and geometric quantization, examining homology stability in algebraic and geometric contexts, including algebraic -theory and the theory of operads.
Empowered by Ancestors
Empowered by Ancestors: Controversy over the Imperial Temple in Song China (960–1279) examines the enduring tension between cultural authority and political power in imperial China by inquiring into Song ritual debates over the Imperial Temple. During these debates, Song-educated elites utilized various discourses to rectify temple rituals in their own ways. In this process, political interests were less emphasized and even detached from ritual discussions. Meanwhile, Song scholars of particular schools developed various ritual theories that were used to reshape society in later periods. Hence, the Song ritual debates exemplified the great transmission of ancestral ritual norms from the to...
Lectures on Differential Geometry
Differential geometry is a subject related to many fields in mathematics and the sciences. The authors of this book provide a vertically integrated introduction to differential geometry and geometric analysis. The material is presented in three distinct parts: an introduction to geometry via submanifolds of Euclidean space, a first course in Riemannian geometry, and a graduate special topics course in geometric analysis, and it contains more than enough content to serve as a good textbook for a course in any of these three topics. The reader will learn about the classical theory of submanifolds, smooth manifolds, Riemannian comparison geometry, bundles, connections, and curvature, the Chern?...
A Short Course in Differential Topology
This book offers a concise and modern introduction to differential topology, the study of smooth manifolds and their properties, at the advanced undergraduate/beginning graduate level. The treatment throughout is hands-on, including many concrete examples and exercises woven into the text with hints provided to guide the student.
