Discrete groups, expanding graphs and invariant measures:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser Verlag
1994
|
| Series: | Progress in Mathematics
125 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 195 Seiten |
| ISBN: | 376435075X 081765075X |
Staff View
MARC
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| 245 | 1 | 0 | |a Discrete groups, expanding graphs and invariant measures |c Alexander Lubotzky. Appendix by Jonathan D. Rogawski |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser Verlag |c 1994 | |
| 300 | |a XI, 195 Seiten | ||
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Record in the Search Index
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| adam_text | Table of Contents
0 Introduction ix
1 Expanding graphs
1.0 Introduction 1
1.1 Expanders and their applications 1
1.2 Existence of expanders 5
2 The Banach Ruziewicz problem
2.0 Introduction 7
2.1 The Hausdorff Banach Tarski paradox 7
2.2 Invariant measures 13
2.3 Notes 18
3 Kazhdan Property (T) and its applications
3.0 Introduction 19
3.1 Kazhdan property (T) for semi simple groups 19
3.2 Lattices and arithmetic subgroups 27
3.3 Explicit construction of expanders using property (T) 30
3.4 Solution of the Ruziewicz problem for Sn, n 4 using
property (T) 34
3.5 Notes 39
4 The Laplacian and its eigenvalues
4.0 Introduction 41
4.1 The geometric Laplacian 41
4.2 The combinatorial Laplacian 44
4.3 Eigenvalues, isoperimetric inequalities and representations ... 49
4.4 Selberg Theorem X ^ and expanders 52
4.5 Random walk on A: regular graphs; Ramanujan graphs 55
4.6 Notes 59
vi Table of Contents
5 The representation theory of PGL2
5.0 Introduction 61
5.1 Representations and spherical functions 62
5.2 Irreducible representations of PSL2(R) and eigenvalues of
the Laplacian 65
5.3 The tree associated with PGL2(Qp) 68
5.4 Irreducible representations of PGL2(Qp) and eigenvalues
of the Hecke operator 70
5.5 Spectral decomposition of F G 72
6 Spectral decomposition of L2(G(Q) G(A))
6.0 Introduction 77
6.1 Deligne s Theorem; adelic formulation 77
6.2 Quaternion algebras and groups 79
6.3 The Strong Approximation Theorem and its applications 81
6.4 Notes 83
7 Banach Ruziewicz problem for n = 2,3; Ramanujan graphs
7.0 Introduction 85
7.1 The spectral decomposition of G (Z[±]) G (IR) x G (Qp) .... 86
7.2 The Banach Ruziewicz problem for n = 2,3 86
7.3 Ramanujan graphs and their extremal properties 88
7.4 Explicit constructions 94
7.5 Notes 99
8 Some more discrete mathematics
8.0 Introduction 101
8.1 The diameter of finite simple groups 101
8.2 Characters and eigenvalues of finite groups 106
8.3 Some more Ramanujan graphs (of unbounded degrees) 112
8.4 Ramanujan diagrams 115
9 Distributing points on the sphere
9.0 Introduction 119
9.1 Hecke operators of group action 119
9.2 Distributing points on S2 (and S3) 121
Table of Contents vii
10 Open problems
10.1 Expanding Graphs 125
10.2 The Banach Ruziewicz Problem 125
10.3 Kazhdan Property (T) and its applications 126
10.4 The Laplacian and its eigenvalues 128
10.5 The representation theory of PGL2 129
10.6 Spectral decomposition of L2(G(Q)/G(A)) 129
10.7 Banach Ruziewitz Problem for n — 2,3; Ramanujan Graphs .. 130
10.8 Some more discrete mathematics 131
10.9 Distributing points on the sphere 133
Appendix: by Jonathan D. Rogawski
Modular forms, the Ramanujan conjecture and the
Jacquet Langlands correspondence
A.O Preliminaries 136
A.I Representation theory and modular forms 139
A.2 Classification of irreducible representations 149
A.3 Quaternion algebras 159
A.4 The Selberg trace formula 164
References to the Appendix 175
References 177
Index 193
|
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| id | DE-604.BV009802213 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:41:07Z |
| institution | BVB |
| isbn | 376435075X 081765075X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006486028 |
| oclc_num | 439608676 |
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| physical | XI, 195 Seiten |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Birkhäuser Verlag |
| record_format | marc |
| series | Progress in Mathematics |
| series2 | Progress in Mathematics Modern Birkhäuser classics |
| spelling | Lubotzky, Alexander 1956- Verfasser (DE-588)172232619 aut Discrete groups, expanding graphs and invariant measures Alexander Lubotzky. Appendix by Jonathan D. Rogawski Basel [u.a.] Birkhäuser Verlag 1994 XI, 195 Seiten txt rdacontent n rdamedia nc rdacarrier Progress in Mathematics 125 Modern Birkhäuser classics Expandierender Graph (DE-588)4352360-2 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Invariantes Maß (DE-588)4352361-4 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 s Expandierender Graph (DE-588)4352360-2 s Invariantes Maß (DE-588)4352361-4 s DE-604 Rogawski, Jonathan D. aut Modular forms, the Ramanujan conjecture and the Jacquet-Langlands correspondence Progress in Mathematics 125 (DE-604)BV000004120 125 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006486028&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lubotzky, Alexander 1956- Rogawski, Jonathan D. Discrete groups, expanding graphs and invariant measures Progress in Mathematics Expandierender Graph (DE-588)4352360-2 gnd Lie-Gruppe (DE-588)4035695-4 gnd Invariantes Maß (DE-588)4352361-4 gnd |
| subject_GND | (DE-588)4352360-2 (DE-588)4035695-4 (DE-588)4352361-4 |
| title | Discrete groups, expanding graphs and invariant measures |
| title_alt | Modular forms, the Ramanujan conjecture and the Jacquet-Langlands correspondence |
| title_auth | Discrete groups, expanding graphs and invariant measures |
| title_exact_search | Discrete groups, expanding graphs and invariant measures |
| title_full | Discrete groups, expanding graphs and invariant measures Alexander Lubotzky. Appendix by Jonathan D. Rogawski |
| title_fullStr | Discrete groups, expanding graphs and invariant measures Alexander Lubotzky. Appendix by Jonathan D. Rogawski |
| title_full_unstemmed | Discrete groups, expanding graphs and invariant measures Alexander Lubotzky. Appendix by Jonathan D. Rogawski |
| title_short | Discrete groups, expanding graphs and invariant measures |
| title_sort | discrete groups expanding graphs and invariant measures |
| topic | Expandierender Graph (DE-588)4352360-2 gnd Lie-Gruppe (DE-588)4035695-4 gnd Invariantes Maß (DE-588)4352361-4 gnd |
| topic_facet | Expandierender Graph Lie-Gruppe Invariantes Maß |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006486028&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
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