Colloquium De Giorgi 2009

Cover......Page 1
Title Page......Page 4
Copyright Page......Page 5
Table of Contents......Page 6
Preface......Page 7
1.1. Cosets and affine maps......Page 14
1.2. Definition of Ap(G)......Page 16
1.3. The connection between cosets and function algebras......Page 19
2. Coset geometry of groups......Page 20
3. An analysis of cosets and coset-preserving maps......Page 22
4. Coset-preserving maps of connected Lie groups......Page 27
5. Isometries of the algebras Ap(G)......Page 28
References......Page 30
Classical analysis and nilpotent Lie groups......Page 32
1. Classical Fourier series......Page 33
2. The Heisenberg group......Page 34
3. Representations and coadjoint orbits......Page 36
4. Square integrable representations......Page 37
5. Commutative spaces – generalities......Page 41
6. Commutative nilmanifolds......Page 43
References......Page 45
1. Basic discourse......Page 46
2. Historical background......Page 48
3. Leibniz conjecture from a modern point of view......Page 50
4. The period ring of Kontsevich......Page 51
5. Schanuel’s conjecture......Page 52
6. Period ring of 1-motifs......Page 53
References......Page 55
The geometry and curvature of shape spaces......Page 56
References......Page 66
Back matter......Page 67