Listen to Coronavirus Patient Zero
Humankind's ever-expanding activities have caused environmental changes that reach beyond localities and regions to become global in scope. Disturbances to the atmosphere, oceans, and land produce changes in the living parts of the planet, while, at the same time, alterations in the biosphere modify the atmosphere, oceans, and land. Understanding this complex web of interactions poses unprecedented intellectual challenges. The atmospheric concentrations of natural trace gases-carbon dioxide (C0 ), methane (CH. ), nitrous oxide (N0), and lower-atmosphere ozone 2 2 (Os)-have increased since the beginning of the industrial revolution. Industrial gases such as the chlorofluorocarbons (CFCs), which are not part of the natural global ecosystem, are increasing at much greater rates than are the naturally occurring trace gases. All these gases absorb and emit infrared radiation and thus have the potential for altering global climate. The major terrestrial biomes are also changing. Although world attention has focused on deforestation, particularly in tropical areas, the development of agriculture, the diversion of water resources, and urbanization have all modified terrestrial ecosystems in both obvious and subtle ways. The terrestrial biosphere, by taking up atmospheric carbon dioxide, acts as a primary determinant of the overall carbon balance of the global ecosystem. Although the ways in which the biosphere absorbs carbon are, as yet, poorly understood, the destruction (and regrowth) of forests certainly alter this process.
Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive exploration of Mumford-Tate groups and domains. Containing basic theory and a wealth of new views and results, it will become an essential resource for graduate students and researchers.
Although Mumford-Tate groups can be defined for general structures, their theory and use to date has mainly been in the classical case of abelian varieties. While the book does examine this area, it focuses on the nonclassical case. The general theory turns out to be very rich, such as in the unexpected connections of finite dimensional and infinite dimensional representation theory of real, semisimple Lie groups. The authors give the complete classification of Hodge representations, a topic that should become a standard in the finite-dimensional representation theory of noncompact, real, semisimple Lie groups. They also indicate that in the future, a connection seems ready to be made between Lie groups that admit discrete series representations and the study of automorphic cohomology on quotients of Mumford-Tate domains by arithmetic groups. Bringing together complex geometry, representation theory, and arithmetic, this book opens up a fresh perspective on an important subject.
Domain Today Articles
Domain Today Books