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Provides a systematic exposition of the modern theory of Gaussian measures. It presents complete and detailed proofs fundamental facts about finite and infinite dimensional Gaussian distributions. Covered topics include linear properties, convexity, linear and nonlinear transformations, and applications to Gaussian and diffusion processes.

Operads are mathematical devices that describe algebraic structures of many varieties and in various categories. Operads are particularly important in categories with a good notion of 'homotopy', where they play a key role in organizing hierarchies of higher homotopies. This book offers an introduction describing the development of operad theory.

Introduces a new research direction in set theory: the study of models of set theory with respect to their extensional overlap or disagreement. The book considers a broad spectrum of objects from analysis, algebra, and combinatorics. The topic is nearly inexhaustible in its variety, and many directions invite further investigation.

The polynomials studied in this book take their origin in number theory. The authors show how, by drawing simple pictures, one can prove some long-standing conjectures and formulate new ones. The theory presented here touches upon many different fields of mathematics.

Mirror symmetry began when theoretical physicists made some astonishing predictions about rational curves on quintic hypersurfaces in four-dimensional projective space. This book presents a comprehensive monograph on mirror symmetry, covering the original observations by the physicists.

Covers geometric analysis on Riemannian symmetric spaces and its relationship to the representation theory of Lie groups. This book covers modern integral geometry for double fibrations. It also discusses the theory of Radon transforms and Fourier transforms on symmetric spaces, inversion formulas, and range theorems.

Introduces a new notion of analytic space over a non-Archimedean field. The book includes a homotopic characterization of the analytic spaces associated with certain classes of algebraic varieties and an interpretation of Bruhat-Tits buildings in terms of these analytic spaces. The author also studies the connection with the earlier notion of a rigid analytic space.