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Introduction to buildings and their geometries with emphasis on model theoretic constructions, covering recent developments.
Buildings are highly structured, geometric objects, primarily used in the finer study of the groups that act upon them. In Buildings and Classical Groups, the author develops the basic theory of buildings and BN-pairs, with a focus on the results needed to apply it to the representation theory of p-adic groups. In particular, he addresses spherical and affine buildings, and the "spherical building at infinity" attached to an affine building. He also covers in detail many otherwise apocryphal results. Classical matrix groups play a prominent role in this study, not only as vehicles to illustrate general results but as primary objects of interest. The author introduces and completely develops terminology and results relevant to classical groups. He also emphasizes the importance of the reflection, or Coxeter groups and develops from scratch everything about reflection groups needed for this study of buildings. In addressing the more elementary spherical constructions, the background pertaining to classical groups includes basic results about quadratic forms, alternating forms, and hermitian forms on vector spaces, plus a description of parabolic subgroups as stabilizers of flags of subspaces. The text then moves on to a detailed study of the subtler, less commonly treated affine case, where the background concerns p-adic numbers, more general discrete valuation rings, and lattices in vector spaces over ultrametric fields. Buildings and Classical Groups provides essential background material for specialists in several fields, particularly mathematicians interested in automorphic forms, representation theory, p-adic groups, number theory, algebraic groups, and Lie theory. No other available source provides such a complete and detailed treatment.
Assembles different theories of motivic integration for the first time, providing all of the necessary background for graduate students and researchers from algebraic geometry, model theory and number theory. In a rapidly-evolving area of research, this volume and Volume 2, which unite the several viewpoints and applications, will prove invaluable.
Classifies the maximal subgroups of the finite groups of Lie type up to dimension 12, using theoretical and computational methods.
A comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic.
Surveys and summaries of the latest research in numerical analysis, optimization, computer algebra and scientific computing.
Review papers from experts in areas of active research into highly oscillatory problems, with an emphasis on computation.
Part two of a two-volume collection exploring recent developments in number theory related to automorphic forms and Galois representations.
A comprehensive collection of expository articles on cutting-edge topics at the forefront of research in algebraic geometry.
A graduate-level introduction to some of the important contemporary ideas and problems in the theory of moduli spaces.