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The concepts of a spin manifold, spinor fields, Dirac operators, and A-genera are presented comprehensively in this book. It also features the development of the theory of Cl-linear elliptic operators and the associated index theorem, which connects certain subtle spin-corbordism invariants to classical questions in geometry.

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(Paperback)

Develops and applies a theory of the ambient metric in conformal geometry. This title includes the derivation of the ambient obstruction tensor and an analysis of the cases of conformally flat and conformally Einstein spaces. It concludes with a construction and characterization of scalar conformal invariants in terms of ambient curvature.

(Paperback)

(Paperback)

Addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies.

(Paperback)

Providing instances of the local Langlands conjecture, this book aims to prove the local Langlands conjecture for GLn over a p-adic field and, to identify the action of the decomposition group at a prime of bad reduction on the l-adic cohomology of the "simple" Shimura varieties.

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The aim of this work is to provide a proof of the nonlinear gravitational stability of the Minkowski space-time. More precisely, the book offers a constructive proof of global, smooth solutions to the Einstein Vacuum Equations, which look, in the large, like the Minkowski space-time. In particular, these solutions are free of black holes and singul

(Hardback)

(Paperback)

Offers a comprehensive account of the Gross-Zagier formula on Shimura curves over real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. This title begins with a conceptual formulation of the Gross-Zagier formula in terms of incoherent quaternion algebras and incoherent automorphic representations.

(Hardback)

Offers a comprehensive account of the Gross-Zagier formula on Shimura curves over real fields relates the heights of Heegner points on abelian varieties to the derivatives of L-series. This title begins with a conceptual formulation of the Gross-Zagier formula in terms of incoherent quaternion algebras and incoherent automorphic representations.

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Presents the analytic foundations to the theory of the hypoelliptic Laplacian. This book shows that the hypoelliptic Laplacian provides a geometric version of the Fokker-Planck equations. It gives the proper functional analytic setting in order to study this operator and develop a pseudodifferential calculus.

(Hardback)

Presents the history in English of the origins and early development of trigonometry. This book identifies the earliest known trigonometric precursors in ancient Egypt, Babylon, and Greece, and examines the revolutionary discoveries of Hipparchus. It traces trigonometry's development into a full-fledged mathematical discipline in India and Islam.

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Kenneth Brakke studies in general dimensions a dynamic system of surfaces of no inertial mass driven by the force of surface tension and opposed by a frictional force proportional to velocity. He formulates his study in terms of varifold surfaces and uses the methods of geometric measure theory to develop a mathematical description of the motion of

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(Paperback)

(Hardback)

(Paperback)

The introduction of the Seiberg-Witten invariants of smooth four-manifolds has revolutionized the study of those manifolds. This book serves as an introduction to the Seiberg-Witten invariants. It also includes a review of the classical material on Spin c structures and their associated Dirac operators.

(Paperback)

Fibre bundles, now an integral part of differential geometry, are also of great importance in modern physics - such as in gauge theory. This book, a succinct introduction to the subject by renown mathematician Norman Steenrod, was the first to present the subject systematically.

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This volume offers a systematic treatment of certain basic parts of algebraic geometry, presented from the analytic and algebraic points of view. The notes focus on comparison theorems between the algebraic, analytic, and continuous categories. Contents include: 1.1 sheaf theory, ringed spaces; 1.2 local structure of analytic and algebraic sets; 1

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(Hardback)

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(Paperback)

There is a well-known correspondence between the objects of algebra and geometry: a space gives rise to a function algebra; a vector bundle over the space corresponds to a projective module over this algebra; cohomology can be read off the de Rham complex; and so on. In this book Yuri Manin addresses a variety of instances in which the application

(Hardback)