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Buildings (Group theory) --- Continuum mechanics --- Continuum mechanics. --- Buildings (Group theory).

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Descent in Buildings begins with the resolution of a major open question about the local structure of Bruhat-Tits buildings. The authors then put their algebraic solution into a geometric context by developing a general fixed point theory for groups acting on buildings of arbitrary type, giving necessary and sufficient conditions for the residues fixed by a group to form a kind of subbuilding or "form" of the original building. At the center of this theory is the notion of a Tits index, a combinatorial version of the notion of an index in the relative theory of algebraic groups. These results are combined at the end to show that every exceptional Bruhat-Tits building arises as a form of a "residually pseudo-split" Bruhat-Tits building. The book concludes with a display of the Tits indices associated with each of these exceptional forms.This is the third and final volume of a trilogy that began with Richard Weiss' The Structure of Spherical Buildings and The Structure of Affine Buildings.

Buildings (Group theory) --- Combinatorial geometry.

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Buildings (Group theory). --- Finite geometries. --- Finite groups.

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This volume contains selected papers by leading researchers from the international conference entitled Tits Buildings and the Model Theory of Groups, held in Würzburg in 2000. The first part of the book provides a general introduction to many aspects of buildings and their geometries, based on short lecture courses given at the conference. The rest of the book comprises survey and research articles on model theoretic results and techniques, showing the vitality and richness of these branches of mathematics. Among the most fruitful techniques, amalgamation constructions à la Hrushovski are explained and classified as they continue to play an important role both in model theory and geometry. The articles succeed in demonstrating the close connection between geometry, group theory and model theory. The book will be invaluable to graduate students as well as experienced researchers working in these areas of mathematics.

Buildings (Group theory) --- Group theory. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Theory of buildings (Group theory) --- Tits's theory of buildings (Group theory) --- Linear algebraic groups

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Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all hooks are again available in paperback. For a complete list of titles, please visit the Princeton University Press website: press.princeton.edu. The most recently published volumes include: Multi-parameter Singular Integrals, by Brian Street, Hangzhou Lectures on Eigenfunctions of the Laplacian, by Christopher D. Sogge, Chow Rings, Decomposition of the Diagonal, and the Topology of Families, by Claire Voisin, Spaces of PL Manifolds and Categories of Simple Maps, by Friedhelm Waldhausen, Bjorn Jahren, and John Rognes, Degenerate Diffusion Operators Arising in Population Biology, by Charles L. Epstein and Rafe Mazzeo, The Gross-Zagier Formula on Shimura Curves, by Xinyi Yuan, Shou-wu Zhang, and Wei Zhang, Mumford-Tate Groups and Domains: Their Geometry and Arithmetic, by Mark Green, Phillip A. Griffiths, and Matt Kerr, The Decomposition of Global Conformal Invariants, by Spyros Alexakis, Some Problems of Unlikely Intersections in Arithmetic and Geometry, by Umberto Zannier, Convolution and Equidistribution: Sato-Fate Theorems for Finite-Field Mellin Transforms, by Nicholas Katz.

Buildings (Group theory) --- Combinatorial geometry --- Geometric combinatorics --- Geometrical combinatorics --- Combinatorial analysis --- Discrete geometry --- Theory of buildings (Group theory) --- Tits's theory of buildings (Group theory) --- Linear algebraic groups