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Five papers by distinguished American and European mathematicians describe some current trends in mathematics in the perspective of the recent past and in terms of expectations for the future. Among the subjects discussed are algebraic groups, quadratic forms, topological aspects of global analysis, variants of the index theorem, and partial differential equations.

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This collection brings together papers by mathematicians exploring the research frontiers of topology. The book covers a wide range of topological specialities.

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Using only the very elementary framework of finite probability spaces, this book treats a number of topics in the modern theory of stochastic processes. This is made possible by using a small amount of Abraham Robinson's nonstandard analysis and not attempting to convert the results into conventional form.

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Offers an examination of the relationship between Radon transforms on symmetric spaces of compact type and the infinitesimal versions of two fundamental rigidity problems in Riemannian geometry. This book focuses on the spectral rigidity problem.

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The description for this book, Ramification Theoretic Methods in Algebraic Geometry (AM-43), will be forthcoming.

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In a series of three papers published in 1930 and 1931, Paley and Zygmund 44 studied a variety of problems concerning series of independent random functions and raised the question of the uniform convergence a.s. of the random Fourier series.

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We shall study a notion of capacity for compact subsets of complex projective space. Our principal motivation for this comes from a theorem of Sibony and Wong 8 , Let K be a compact circled subset of the unit sphere in C2.

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Gives a unified treatment of the construction of fixed-points for renormalization and the construction of hyperbolic 3- manifolds fibering over the circle. This approach shows open hyperbolic manifolds are inflexible, and yields quantitative counterparts to Mostow rigidity.

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This volume contains papers and abstracts by participants of the Conference on Riemann Surfaces and Related Topics, which was held at the State University of New York at Stony Brook, June 5-9, 1978.

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The author introduced the concept of a "local system" on P1-{a finite set of points} nearly 140 years ago. His idea was to study nth order linear differential equations by studying the rank n local systems (of local holomorphic solutions) to which they gave rise.

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Represents the asymptotic analysis, via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrodinger equation in the semiclassical asymptotic regime. This book exploits complete integrability to establish pointwise asymptotics for this problem's solution in the semiclassical regime.

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The description for this book, Seminar on Atiyah-Singer Index Theorem. (AM-57), will be forthcoming.

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The description for this book, Seminar On Minimal Submanifolds. (AM-103), will be forthcoming.

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The description for this book, Seminar on Transformation Groups. (AM-46), will be forthcoming.

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The description for this book, Singular Points of Complex Hypersurfaces. (AM-61), will be forthcoming.

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Considers the so-called Unlikely Intersections, a topic that embraces well-known issues, such as Lang's and Manin-Mumford's, concerning torsion points in subvarieties of tori or abelian varieties. This book considers algebraic subgroups that meet a given subvariety in a set of unlikely dimension.

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Since its introduction by Friedhelm Waldhausen in the 1970s, the algebraic K-theory of spaces has been recognized as the main tool for studying parametrized phenomena in the theory of manifolds. However, a full proof of the equivalence relating the two areas has not appeared until now. This book presents such a proof, essentially completing Waldhau

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Proves an analogue of Thurston's celebrated hyperbolic Dehn surgery theorem in the context of complex hyperbolic discrete groups, and then derives two main geometric consequences from it. This book is suitable for graduate students interested in this area of research, as well as researchers in allied fields such as Kleinian groups and CR geometry.