E-Book, Englisch, 329 Seiten
Holden / Piene The Abel Prize
1. Auflage 2009
ISBN: 978-3-642-01373-7
Verlag: Springer
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
2003-2007 The First Five Years
E-Book, Englisch, 329 Seiten
ISBN: 978-3-642-01373-7
Verlag: Springer
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
Each laureate provides an autobiography or an interview, a curriculum vitae, and a complete bibliography. This is complemented by a scholarly description of their work written by leading experts in the field and by a brief history of the Abel Prize. Interviews with the laureates can be found at http://extras.springer.com .
Autoren/Hrsg.
Weitere Infos & Material
1;Preface;5
2;Contents;7
3;The History of the Abel Prize and the Honorary Abel Prize;12
3.1;The History of the Abel Prize;13
3.1.1;References;18
3.2;2002-an Honorary Abel Prize to Atle Selberg;19
3.2.1;References;21
4;2003 Jean-Pierre Serre;22
4.1;Jean-Pierre Serre: Mon premier demi-siècle au Collège de France;23
4.2;Jean-Pierre Serre: An Overview of His Work;42
4.2.1;Introduction;42
4.2.2;The Beginnings;43
4.2.2.1;Homotopy Groups of Spheres;44
4.2.2.2;Hochschild-Serre Spectral Sequence;45
4.2.2.3;Sheaf Cohomology of Complex Manifolds;45
4.2.2.4;The Amsterdam Congress;46
4.2.3;Sheaf Cohomology;46
4.2.3.1;FAC;46
4.2.3.2;GAGA;47
4.2.3.3;Cohomology of Algebraic Varieties;47
4.2.4;Lie Groups and Lie Algebras;49
4.2.5;Local Algebra;50
4.2.6;Projective Modules;50
4.2.7;Algebraic Number Fields;51
4.2.8;Class Field Theory;52
4.2.8.1;Geometric Class Field Theory;52
4.2.8.2;Local Class Field Theory;54
4.2.8.3;A Local Mass Formula;55
4.2.9;p-adic Analysis;55
4.2.10;Group Cohomology;56
4.2.10.1;Cohomology of Profinite Groups and p-adic Lie Groups;56
4.2.10.2;Galois Cohomology;57
4.2.10.3;Galois Cohomology of Linear Algebraic Groups;57
4.2.10.4;Self-dual Normal Basis;59
4.2.10.5;Essential Dimension;59
4.2.11;Discrete Subgroups;60
4.2.11.1;Congruence Subgroups;61
4.2.11.2;Cohomology of Arithmetic Groups;62
4.2.12;Arithmetic of Algebraic Varieties;63
4.2.12.1;Modular Curves;63
4.2.12.2;Varieties Over Finite Fields;65
4.2.12.3;Number of Points of Curves Over Finite Fields;65
4.2.12.4;Diophantine Problems;67
4.2.13;Field Theory;68
4.2.14;Galois Representations;71
4.2.14.1;Hodge-Tate Modules;71
4.2.14.2;Elliptic Curves and l-adic Representations;71
4.2.14.3;Modular Forms and l-adic Representations;74
4.2.14.4;Abelian Varieties and l-adic Representations;78
4.2.14.5;Motives;81
4.2.15;Group Theory;82
4.2.15.1;Representation Theory;82
4.2.15.2;Algebraic Groups;85
4.2.15.3;Finite Subgroups of Lie Groups and of Algebraic Groups;86
4.2.16;Miscellaneous Writings;87
4.2.17;References;89
4.3;List of Publications for Jean-Pierre Serre;90
4.4;Curriculum Vitae for Jean-Pierre Serre;103
5;2004 Sir Michael Atiyah and Isadore M. Singer;105
5.1;Autobiography;106
5.2;Autobiography;115
5.3;The Atiyah-Singer Index Theorem;121
5.3.1;Introduction;121
5.3.2;Background;121
5.3.2.1;The Index;121
5.3.2.2;Riemann-Roch;122
5.3.2.3;The Beginning;123
5.3.2.4;The Signature;124
5.3.2.5;Hirzebruch-Riemann-Roch;127
5.3.2.6;The Dirac Operator;129
5.3.3;The Integer Index;132
5.3.3.1;Formulation of the Theorem;132
5.3.3.2;Integrality Theorems;134
5.3.3.3;Positive Scalar Curvature;135
5.3.3.4;Gauge-Theoretic Moduli Spaces;136
5.3.4;The Equivariant Index;138
5.3.4.1;K-Theory;138
5.3.4.2;Fixed Point Theorems;140
5.3.4.3;Rigidity Theorems;143
5.3.5;The mod 2 Index;145
5.3.5.1;Real K-Theory;145
5.3.5.2;Theta Characteristics;146
5.3.5.3;Positive Scalar Curvature;146
5.3.6;The Index for Families;147
5.3.6.1;Fredholm Operators;147
5.3.6.2;Jumping of Dimension;148
5.3.7;The Local Index Theorem;150
5.3.7.1;The Heat Kernel;150
5.3.7.2;The Eta Invariant;152
5.3.7.3;Quantum Field Theory;153
5.3.7.4;The Supersymmetric Proof;154
5.3.8;References;155
5.4;List of Publications for Sir Michael Atiyah;157
5.5;List of Publications for Isadore M. Singer;170
5.6;Curriculum Vitae for Sir Michael Francis Atiyah, OM, FRS, FRSE;177
5.7;Curriculum Vitae for Isadore Manual Singer;181
6;2005 Peter D. Lax;183
6.1;Autobiography;184
6.2;A Survey of Peter D. Lax's Contributions to Mathematics;191
6.2.1;Introduction;191
6.2.2;Partial Differential Equations-General Results;193
6.2.3;Difference Approximations to Partial Differential Equations;197
6.2.4;Hyperbolic Systems of Conservation Laws;198
6.2.5;Integrable Systems;205
6.2.6;Lax-Phillips Scattering Theory;210
6.2.7;References;213
6.3;List of Publications for Peter D. Lax;217
6.4;Curriculum Vitae for Peter David Lax;230
7;2006 Lennart Carleson;232
7.1;Reflections on My Life as a Mathematician;233
7.2;Carleson for Beginners;240
7.2.1;References;267
7.3;List of Publications for Lennart Carleson;268
7.4;Curriculum Vitae for Lennart Axel Edvard Carleson;273
8;2007 S.R. Srinivasa Varadhan;275
8.1;Autobiography;276
8.2;A Personal Perspective on Raghu Varadhan's Role in the Development of Stochastic Analysis;284
8.2.1;A Great Day for the Coin Flippers;284
8.2.2;Stochastic Analysis;284
8.2.3;Varadhan;287
8.2.4;Independent or Uncorrelated;287
8.2.4.1;A Simple Example;288
8.2.5;Diffusion Equations and PDE;291
8.2.5.1;Elliptic PDEs in Non-divergence Form with Continuous Elliptic Coefficients-Uniqueness of Solution;292
8.2.5.2;First-Order PDEs and Large Deviations;294
8.2.5.3;PDEs and Probability in the 60s;295
8.2.6;The Support Theorem-Understanding the Itô Differential Equation;296
8.2.6.1;On Extending the Wong-Zakai Theorem;296
8.2.6.1.1;One-Dimension of Rough Control;299
8.2.6.1.2;Multiple Dimensions of Rough Control;300
8.2.7;The Donsker-Varadhan Theory of Large Deviations;301
8.2.7.1;Short Time Behaviour-Geodesics;302
8.2.7.2;Long Time Behaviour-Occupation Measures;305
8.2.8;Hydrodynamical Limits, Interacting Particles and Other Questions;306
8.2.8.1;Homogenised Hamilton-Jacobi Equations;307
8.2.9;Conclusion;307
8.2.10;References;308
8.3;List of Publications for S.R. Srinivasa Varadhan;310
8.4;Curriculum Vitae for Sathamangalam Rangaiyenga Srinivasa Varadhan;318
9;The Abel Committee;320
10;The Board for the Niels Henrik Abel Memorial Fund;322
