A number of important topics in complex analysis and geometry are covered in this excellent introductory text. Written by experts in the subject, each chapter unfolds from the basics to the more complex. The exposition is rapid-paced and efficient, without compromising proofs and examples that enable the reader to grasp the essentials. The most basic type of domain examined is the bounded symmetric domain, originally described and classified by Cartan and Harish- Chandra. Two of the five parts of the text deal with these domains: one introduces the subject through the theory of semisimple Lie algebras (Koranyi), and the other through Jordan algebras and triple systems (Roos). Larger classes of domains and spaces are furnished by the pseudo-Hermitian symmetric spaces and related R-spaces. These classes are covered via a study of their geometry and a presentation and classification of their Lie algebraic theory (Kaneyuki). In the fourth part of the book, the heat kernels of the symmetric spaces belonging to the classical Lie groups are determined (Lu). Explicit computations are made for each case, giving precise results and complementing the more abstract and general methods presented. Also explored are recent developments in the field, in particular, the study of complex semigroups which generalize complex tube domains and function spaces on them (Faraut). This volume will be useful as a graduate text for students of Lie group theory with connections to complex analysis, or as a self-study resource for newcomers to the field. Readers will reach the frontiers of the subject in a considerably shorter time than with existing texts.
This volume presents the proceedings of the workshop "Harmonic Functions on Graphs" held at the Graduate Centre of CUNY in the autumn of 1995. The main papers present material from four minicourses given by leading experts: D. Cartwright, A. Figà-Talamanca, S. Sawyer, and T. Steger. These minicrouses are introductions which gradually progress to deeper and less known branches of the subject. One of the topics treated is buildings, which are discrete analogues of symmetric spaces of arbitrary rank; buildings of rank are trees. Harmonic analysis on buildings is a fairly new and important field of research. One of the minicourses discusses buildings from the combinatorial perspective and another examines them from the p-adic perspective. the third minicourse deals with the connections of trees with p-adic analysis, and the fourth deals with random walks, ie., with the probabilistic side of harmonic functions on trees. The book also contains the extended abstracts of 19 of the 20 lectures given by the participants on their recent results. These abstracts, well detailed and clearly understandable, give a good cross-section of the present state of research in the field.
This book’s great service is that it challenges us to consider the ways in which our institutions and systems, and the assumptions, positions and divisions that undergird them, leave us ill prepared for the next crisis."—Robert Rubin, The New York Times Book Review "Full of valuable insight and telling details, this may well be the best thing to read if you want to know what happened in 2020." --Paul Krugman, New York Review of Books Deftly weaving finance, politics, business, and the global human experience into one tight narrative, a tour-de-force account of 2020, the year that changed everything--from the acclaimed author of Crashed. The shocks of 2020 have been great and small, disrupting the world economy, international relations and the daily lives of virtually everyone on the planet. Never before has the entire world economy contracted by 20 percent in a matter of weeks nor in the historic record of modern capitalism has there been a moment in which 95 percent of the world's economies were suffering all at the same time. Across the world hundreds of millions have lost their jobs. And over it all looms the specter of pandemic, and death. Adam Tooze, whose last book was universally lauded for guiding us coherently through the chaos of the 2008 crash, now brings his bravura analytical and narrative skills to a panoramic and synthetic overview of our current crisis. By focusing on finance and business, he sets the pandemic story in a frame that casts a sobering new light on how unprepared the world was to fight the crisis, and how deep the ruptures in our way of living and doing business are. The virus has attacked the economy with as much ferocity as it has our health, and there is no vaccine arriving to address that. Tooze's special gift is to show how social organization, political interests, and economic policy interact with devastating human consequences, from your local hospital to the World Bank. He moves fluidly from the impact of currency fluctuations to the decimation of institutions--such as health-care systems, schools, and social services--in the name of efficiency. He starkly analyzes what happened when the pandemic collided with domestic politics (China's party conferences; the American elections), what the unintended consequences of the vaccine race might be, and the role climate change played in the pandemic. Finally, he proves how no unilateral declaration of 'independence" or isolation can extricate any modern country from the global web of travel, goods, services, and finance.
For a world mired in catastrophe, nothing could be more urgent than the question of survival. In this theoretically and methodologically groundbreaking book, Adam Y. Stern calls for a critical reevaluation of survival as a contemporary regime of representation. In Survival, Stern asks what texts, what institutions, and what traditions have made survival a recognizable element of our current political vocabulary. The book begins by suggesting that the interpretive key lies in the discursive prominence of "Jewish survival." Yet the Jewish example, he argues, is less a marker of Jewish history than an index of Christianity's impact on the modern, secular, political imagination. With this inversion, the book repositions Jewish survival as the supplemental effect and mask of a more capacious political theology of Christian survival. The argument proceeds by taking major moments in twentieth-century philosophy, theology, and political theory as occasions for collecting the scattered elements of survival's theological-political archive. Through readings of canonical texts by secular and Jewish thinkers—Hannah Arendt, Walter Benjamin, Franz Rosenzweig, and Sigmund Freud—Stern shows that survival belongs to a history of debates about the sovereignty and subjection of Christ's body. Interrogating survival as a rhetorical formation, the book intervenes in discussions about biopolitics, secularism, political theology, and the philosophy of religion.
A number of important topics in complex analysis and geometry are covered in this excellent introductory text. Written by experts in the subject, each chapter unfolds from the basics to the more complex. The exposition is rapid-paced and efficient, without compromising proofs and examples that enable the reader to grasp the essentials. The most basic type of domain examined is the bounded symmetric domain, originally described and classified by Cartan and Harish- Chandra. Two of the five parts of the text deal with these domains: one introduces the subject through the theory of semisimple Lie algebras (Koranyi), and the other through Jordan algebras and triple systems (Roos). Larger classes of domains and spaces are furnished by the pseudo-Hermitian symmetric spaces and related R-spaces. These classes are covered via a study of their geometry and a presentation and classification of their Lie algebraic theory (Kaneyuki). In the fourth part of the book, the heat kernels of the symmetric spaces belonging to the classical Lie groups are determined (Lu). Explicit computations are made for each case, giving precise results and complementing the more abstract and general methods presented. Also explored are recent developments in the field, in particular, the study of complex semigroups which generalize complex tube domains and function spaces on them (Faraut). This volume will be useful as a graduate text for students of Lie group theory with connections to complex analysis, or as a self-study resource for newcomers to the field. Readers will reach the frontiers of the subject in a considerably shorter time than with existing texts.
The present book is the first to treat analysis on symmetric cones in a systematic way. It starts by describing, with the simplest available proofs, the Jordan algebra approach to the geometric and algebraic foundations of the theory due to M. Koecher and his school. In subsequent parts itdiscusses harmonic analysis and special functions associated to symmetric cones; it also tries these results together with the study of holomorphic functions on bounded symmetric domains of tube type. It contains a number of new results and new proofs of old results.
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