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34925 results in Mathematics (general)

Page 78 of 1747

  • 12 - Reduction Theory for Adelic Coset Spaces

  • Joachim Schwermer, Universität Wien, Austria
  • Book:
    Reduction Theory and Arithmetic Groups
    Published online:
    01 December 2022
    Print publication:
    15 December 2022, pp 274-296

  • Summary

    Arithmetic groups are generalisations, to the setting of algebraic groups over a global field, of the subgroups of finite index in the general linear group with entries in the ring of integers of an algebraic number field. They are rich, diverse structures, and they arise in many areas of study.

    This text enables you to build a solid, rigorous foundation in the subject. It first develops essential geometric and number of theoretical components to the investigations of arithmetic groups and then examines a number of different themes, including reduction theory, (semi)-stable lattices, arithmetic groups in forms of the special linear group, unipotent groups and tori, and reduction theory for adelic coset spaces. Also included is a thorough treatment of the construction of geometric cycles in arithmetically defined locally symmetric spaces and some associated cohomological questions. Written by a renowned expert, this book will be a valuable reference for researchers and graduate students alike.

  • 11 - Geometric Cycles via Rational Automorphisms

  • Joachim Schwermer, Universität Wien, Austria
  • Book:
    Reduction Theory and Arithmetic Groups
    Published online:
    01 December 2022
    Print publication:
    15 December 2022, pp 249-273

  • Summary

    Arithmetic groups are generalisations, to the setting of algebraic groups over a global field, of the subgroups of finite index in the general linear group with entries in the ring of integers of an algebraic number field. They are rich, diverse structures, and they arise in many areas of study.

    This text enables you to build a solid, rigorous foundation in the subject. It first develops essential geometric and number of theoretical components to the investigations of arithmetic groups and then examines a number of different themes, including reduction theory, (semi)-stable lattices, arithmetic groups in forms of the special linear group, unipotent groups and tori, and reduction theory for adelic coset spaces. Also included is a thorough treatment of the construction of geometric cycles in arithmetically defined locally symmetric spaces and some associated cohomological questions. Written by a renowned expert, this book will be a valuable reference for researchers and graduate students alike.

  • 4 - Arithmetic Groups

  • Joachim Schwermer, Universität Wien, Austria
  • Book:
    Reduction Theory and Arithmetic Groups
    Published online:
    01 December 2022
    Print publication:
    15 December 2022, pp 90-121

  • Summary

    Arithmetic groups are generalisations, to the setting of algebraic groups over a global field, of the subgroups of finite index in the general linear group with entries in the ring of integers of an algebraic number field. They are rich, diverse structures, and they arise in many areas of study.

    This text enables you to build a solid, rigorous foundation in the subject. It first develops essential geometric and number of theoretical components to the investigations of arithmetic groups and then examines a number of different themes, including reduction theory, (semi)-stable lattices, arithmetic groups in forms of the special linear group, unipotent groups and tori, and reduction theory for adelic coset spaces. Also included is a thorough treatment of the construction of geometric cycles in arithmetically defined locally symmetric spaces and some associated cohomological questions. Written by a renowned expert, this book will be a valuable reference for researchers and graduate students alike.

  • 5 - Arithmetically Defined Kleinian Groups and Hyperbolic 3-Space

  • Joachim Schwermer, Universität Wien, Austria
  • Book:
    Reduction Theory and Arithmetic Groups
    Published online:
    01 December 2022
    Print publication:
    15 December 2022, pp 122-138

  • Summary

    Arithmetic groups are generalisations, to the setting of algebraic groups over a global field, of the subgroups of finite index in the general linear group with entries in the ring of integers of an algebraic number field. They are rich, diverse structures, and they arise in many areas of study.

    This text enables you to build a solid, rigorous foundation in the subject. It first develops essential geometric and number of theoretical components to the investigations of arithmetic groups and then examines a number of different themes, including reduction theory, (semi)-stable lattices, arithmetic groups in forms of the special linear group, unipotent groups and tori, and reduction theory for adelic coset spaces. Also included is a thorough treatment of the construction of geometric cycles in arithmetically defined locally symmetric spaces and some associated cohomological questions. Written by a renowned expert, this book will be a valuable reference for researchers and graduate students alike.

  • 9 - Arithmetic Groups, Ambient Lie Groups, and Related Geometric Objects

  • Joachim Schwermer, Universität Wien, Austria
  • Book:
    Reduction Theory and Arithmetic Groups
    Published online:
    01 December 2022
    Print publication:
    15 December 2022, pp 202-236

  • Summary

    Arithmetic groups are generalisations, to the setting of algebraic groups over a global field, of the subgroups of finite index in the general linear group with entries in the ring of integers of an algebraic number field. They are rich, diverse structures, and they arise in many areas of study.

    This text enables you to build a solid, rigorous foundation in the subject. It first develops essential geometric and number of theoretical components to the investigations of arithmetic groups and then examines a number of different themes, including reduction theory, (semi)-stable lattices, arithmetic groups in forms of the special linear group, unipotent groups and tori, and reduction theory for adelic coset spaces. Also included is a thorough treatment of the construction of geometric cycles in arithmetically defined locally symmetric spaces and some associated cohomological questions. Written by a renowned expert, this book will be a valuable reference for researchers and graduate students alike.

  • 1 - Modules, Lattices, and Orders

  • Joachim Schwermer, Universität Wien, Austria
  • Book:
    Reduction Theory and Arithmetic Groups
    Published online:
    01 December 2022
    Print publication:
    15 December 2022, pp 3-45

  • Summary

    Arithmetic groups are generalisations, to the setting of algebraic groups over a global field, of the subgroups of finite index in the general linear group with entries in the ring of integers of an algebraic number field. They are rich, diverse structures, and they arise in many areas of study.

    This text enables you to build a solid, rigorous foundation in the subject. It first develops essential geometric and number of theoretical components to the investigations of arithmetic groups and then examines a number of different themes, including reduction theory, (semi)-stable lattices, arithmetic groups in forms of the special linear group, unipotent groups and tori, and reduction theory for adelic coset spaces. Also included is a thorough treatment of the construction of geometric cycles in arithmetically defined locally symmetric spaces and some associated cohomological questions. Written by a renowned expert, this book will be a valuable reference for researchers and graduate students alike.

  • 6 - Lattices: Reduction Theory for GLn

  • Joachim Schwermer, Universität Wien, Austria
  • Book:
    Reduction Theory and Arithmetic Groups
    Published online:
    01 December 2022
    Print publication:
    15 December 2022, pp 141-151

  • Summary

    Arithmetic groups are generalisations, to the setting of algebraic groups over a global field, of the subgroups of finite index in the general linear group with entries in the ring of integers of an algebraic number field. They are rich, diverse structures, and they arise in many areas of study.

    This text enables you to build a solid, rigorous foundation in the subject. It first develops essential geometric and number of theoretical components to the investigations of arithmetic groups and then examines a number of different themes, including reduction theory, (semi)-stable lattices, arithmetic groups in forms of the special linear group, unipotent groups and tori, and reduction theory for adelic coset spaces. Also included is a thorough treatment of the construction of geometric cycles in arithmetically defined locally symmetric spaces and some associated cohomological questions. Written by a renowned expert, this book will be a valuable reference for researchers and graduate students alike.

  • 2 - The General Linear Group over Rings

  • Joachim Schwermer, Universität Wien, Austria
  • Book:
    Reduction Theory and Arithmetic Groups
    Published online:
    01 December 2022
    Print publication:
    15 December 2022, pp 46-69

  • Summary

    Arithmetic groups are generalisations, to the setting of algebraic groups over a global field, of the subgroups of finite index in the general linear group with entries in the ring of integers of an algebraic number field. They are rich, diverse structures, and they arise in many areas of study.

    This text enables you to build a solid, rigorous foundation in the subject. It first develops essential geometric and number of theoretical components to the investigations of arithmetic groups and then examines a number of different themes, including reduction theory, (semi)-stable lattices, arithmetic groups in forms of the special linear group, unipotent groups and tori, and reduction theory for adelic coset spaces. Also included is a thorough treatment of the construction of geometric cycles in arithmetically defined locally symmetric spaces and some associated cohomological questions. Written by a renowned expert, this book will be a valuable reference for researchers and graduate students alike.

  • 7 - Reduction Theory and (Semi)-Stable Lattices

  • Joachim Schwermer, Universität Wien, Austria
  • Book:
    Reduction Theory and Arithmetic Groups
    Published online:
    01 December 2022
    Print publication:
    15 December 2022, pp 152-173

  • Summary

    Arithmetic groups are generalisations, to the setting of algebraic groups over a global field, of the subgroups of finite index in the general linear group with entries in the ring of integers of an algebraic number field. They are rich, diverse structures, and they arise in many areas of study.

    This text enables you to build a solid, rigorous foundation in the subject. It first develops essential geometric and number of theoretical components to the investigations of arithmetic groups and then examines a number of different themes, including reduction theory, (semi)-stable lattices, arithmetic groups in forms of the special linear group, unipotent groups and tori, and reduction theory for adelic coset spaces. Also included is a thorough treatment of the construction of geometric cycles in arithmetically defined locally symmetric spaces and some associated cohomological questions. Written by a renowned expert, this book will be a valuable reference for researchers and graduate students alike.

Modern Mathematical Logic
  • Joseph Mileti
  • Published online:
    08 December 2022
    Print publication:
    22 September 2022
  • This textbook gives a complete and modern introduction to mathematical logic. The author uses contemporary notation, conventions, and perspectives throughout, and emphasizes interactions with the rest of mathematics. In addition to covering the basic concepts of mathematical logic and the fundamental material on completeness, compactness, and incompleteness, it devotes significant space to thorough introductions to the pillars of the modern subject: model theory, set theory, and computability. Requiring only a modest background of undergraduate mathematics, the text can be readily adapted for a variety of one- or two-semester courses at the upper-undergraduate or beginning-graduate level. Numerous examples reinforce the key ideas and illustrate their applications, and a wealth of classroom-tested exercises serve to consolidate readers' understanding. Comprehensive and engaging, this book offers a fresh approach to this enduringly fascinating and important subject.

An Introduction to Infinite-Dimensional Differential Geometry
  • Alexander Schmeding
  • Published online:
    08 December 2022
    Print publication:
    22 December 2022
  • Introducing foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, this text is based on Bastiani calculus. It focuses on two main areas of infinite-dimensional geometry: infinite-dimensional Lie groups and weak Riemannian geometry, exploring their connections to manifolds of (smooth) mappings. Topics covered include diffeomorphism groups, loop groups and Riemannian metrics for shape analysis. Numerous examples highlight both surprising connections between finite- and infinite-dimensional geometry, and challenges occurring solely in infinite dimensions. The geometric techniques developed are then showcased in modern applications of geometry such as geometric hydrodynamics, higher geometry in the guise of Lie groupoids, and rough path theory. With plentiful exercises, some with solutions, and worked examples, this will be indispensable for graduate students and researchers working at the intersection of functional analysis, non-linear differential equations and differential geometry. This title is also available as Open Access on Cambridge Core.

Page 78 of 1747