ISSN 0002-9920 Notices of the American Mathematical Society ABCD springer.com Post Mathematics and Quantum NEW Culture VI NEW Cryptography The latest in this Springer This book introduces the series probes the interplay reader to the next generation of between mathematics and of the American Mathematical Society cryptographic algorithms, the systems the worlds of art, cinema, theatre and that resist quantum-computer attacks: history, medicine, biology and April 2009 Volume 56, Number 4 in particular, post-quantum public-key aeronautics. Series Editor Michele encryption systems and post-quantum Emmer has chosen essays illuminating public-key signature systems. Leading experts have joined these connections in fascinating ways. forces for the fi rst time to explain the state of the art in 2009. X, 299 p. 136 illus., 14 in color. 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Krantz, Washington University, Gregory S. Chirikjian, The John Hopkins Germany St. Louis, MO, USA University, Baltimore, MD, USA This book studies structural properties of This self-contained text provides an intro- The subjects of stochastic processes, Q-curvature from an extrinsic point of view duction to modern harmonic analysis in information theory, and Lie groups are by regarding it as a derived quantity of the context in which it is actually applied, usually treated separately from each other. certain conformally covariant families of dif- in particular, through complex function This unique textbook presents these topics ferential operators which are associated to theory and partial differential equations. It in a unifi ed setting, thereby building bridg- hypersurfaces. The new approach is at the takes the novice mathematical reader from es among fi elds that are rarely studied by cutting edge of central developments in the rudiments of harmonic analysis (Fourier the same individuals. Volume I establishes conformal differential geometry in the last series) to the Fourier transform, pseudo- the geometric and statistical foundations two decades (Fefferman-Graham ambient differential operators, and fi nally to Heisen- required to understand the fundamentals metrics, spectral theory on Poincaré- berg analysis. Within the textbook, the of continuous-time stochastic processes, Einstein spaces, tractor calculus, Verma new ideas on the Heisenberg group are differential geometry, and the statistical modules and Cartan geometry). The theory applied to the study of estimates for both branch of information theory. of conformally covariant families is inspired the Szegö and Poisson–Szegö integrals on by the idea of holography in the AdS/CFT- 2009. APPROX. 410 P. 15 ILLUS. HARDCOVER the unit ball in complex space. duality. Among other things, it naturally ISBN 978-0-8176-4802-2 CA. $54.95 leads to a holographic description of Q- 2009. XIV, 360 P. 26 ILLUS. HARDCOVER APPLIED AND NUMERICAL HARMONIC curvature. The methods admit generaliza- ISBN 978-0-8176-4668-4 CA. $69.95 ANALYSIS APPLIED AND NUMERICAL HARMONIC tions in various directions. ANALYSIS 2009. APPROX. 500 P. HARDCOVER Mathematics ISBN 978-3-7643-9899-6 $119.00 Distributions for Multimedia PROGRESS IN MATHEMATICS, VOL. 275 Theory and Applications M. Victor Wickerhauser, Washington University, St. Louis, MO, USA Nonlinear Partial Johannes J. Duistermaat; Johan A.C. Kolk, Universiteit Utrecht, The Netherlands This textbook presents the mathematics Differential Equations that is foundational