Title The Abel Prize 2008-2012 / edited by Helge Holden, Ragni Piene

Published Heidelberg : Springer, 2014

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Description 1 online resource (xvii, 571 pages) : illustrations (some color) Contents 880-01 Preface -- K.G. Helsvig: The Abel Prize -- the Missing Nobel in Mathematics.- 2008 John G. Thompson and Jacques Tits: J.G. Thompson: Some Reflections.- R. Lyons and R.M. Guralnick: The Work of John Griggs Tompson: A Survey -- List of Publications for John G. Thompson -- Curriculum Vitae for John G. Thompson -- F. Buekenhout: A biography of Jacques Tits -- F. Buekenhout: A Report on the Scientific Contributions of Jacques Tits -- List of Publications -- Curriculum Vitae -- 2009 Misha Gromov: M. Gromov: A Few Recollections -- D. Burago, and Ya. Eliashberg (Eds.): A Few Snapshots From the Work of Mikhail Gromov -- List of Publications -- Curriculum Vitae -- 2010 John T. Tate Jr.: J. Tate: An Autobiography -- J.S. Milne: The Work of John Tate -- List of Publications -- Curriculum Vitae -- 2011 John W. Milnor: J. Milnor: Autobiography -- H. Bass: Milnor's Work in Algebra and Its Ramifications -- M. Lyubich: John Milnor's Work in Dynamics -- L.C. Siebenmann: John W. Milnor's Work on the Classification of Differentiable Manifolds -- List of Publications -- Curriculum Vitae -- 2012 Endre Szemerédi.: E. Szemerédi: Autobiography -- W.T. Gowers: The Mathematics of Endre Szemerédi -- List of Publications -- Curriculum Vitae -- A Letter by Niels Henrik Abel to August Leopold Crelle -- C. Skau: Abel and the Theory of Algebraic Equations -- Appendices: The Abel Committee -- The Niels Henrik Abel Board -- The Abel Lectures 2003-2012 -- The Abel Presenters 2003-2012.- Addenda, Errata and Updates 880-01/(S Contents note continued: 2.15. Comments on Motivation and Strategy / L.C. Siebenmann -- 2.16. Smale's Dramatic Explanation of Milnor's 'deus ex machina' / L.C. Siebenmann -- 3. Early Achievements of Surgery / L.C. Siebenmann -- 3.1. Rough Description of Surgery / L.C. Siebenmann -- 3.2. Springtime of Surgery / L.C. Siebenmann -- 3.3. First Flowering of Surgery / L.C. Siebenmann -- 3.4. Exact Sequence Entrapping Θn for n> or = to 5 / L.C. Siebenmann -- 3.5. Analysis of the Subgroup bP of Θn / L.C. Siebenmann -- 3.6. Complements Concerning Boundaries of Parallelizable Manifolds / L.C. Siebenmann -- 4. Metamorphosis / L.C. Siebenmann -- 4.1. Milnor's Microbundles / L.C. Siebenmann -- 4.2. Surgery for Classical Smooth Manifolds / L.C. Siebenmann -- 4.3. Further Extensions of Surgery / L.C. Siebenmann -- 4.4. Conjectures / L.C. Siebenmann -- References / L.C. Siebenmann -- List of Publications for John Willard Milnor / L.C. Siebenmann -- Curriculum Vitae for John Willard Milnor / L.C. Siebenmann -- Autobiography / L.C. Siebenmann -- Mathematics of Endre Szemeredi / Endre Szemerédi -- 1. Introduction / W.T. Gowers -- 2. Szemerédi's Theorem / W.T. Gowers -- 2.1. Sketch Proof of Szemerédi's Theorem when k = 3 / W.T. Gowers -- 2.2. What Happens when the Progressions Are Longer/ W.T. Gowers -- 3. Szemerédi's Regularity Lemma / W.T. Gowers -- 3.1. Quasirandom Graphs and the Counting Lemma / W.T. Gowers -- 3.2. Statement of the Regularity Lemma / W.T. Gowers -- 3.3. Sketch Proof of the Regularity Lemma / W.T. Gowers -- 3.4. Regularity Lemma and Szemerédi's Theorem / W.T. Gowers -- 4. Triangle Removal Lemma / W.T. Gowers -- 4.1. Sketch Proof of the Triangle Removal Lemma / W.T. Gowers -- 4.2. Applications of the Triangle Removal Lemma / W.T. Gowers -- 5. Sharp Upper Bound for the Ramsey Number R(3, k) / W.T. Gowers -- 5.1. Choosing an Independent Set More Carefully / W.T. Gowers -- 6. Counterexample to Heilbronn's Triangle Conjecture / W.T. Gowers -- 7. Optimal Parallel Sorting Network / W.T. Gowers -- 8. Theorem on Point-Line Incidences / W.T. Gowers -- 8.1. Székely's Proof of the Szemerédi-Trotter Theorem / W.T. Gowers -- 8.2. Application of the Szemerédi-Trotter Theorem / W.T. Gowers -- 8.3. What Are the Extremal Sets in the Szemerédi-Trotter Theorem/ W.T. Gowers -- 9. Probability that a Random ±1 Matrix is Singular / W.T. Gowers -- 9.1. Need to Consider Dependences / W.T. Gowers -- 9.2. Main Idea / W.T. Gowers -- 9.3. Subsequent Improvements / W.T. Gowers -- 10. Conclusion / W.T. Gowers -- References / W.T. Gowers -- List of Publications for Endre Szemeredi / W.T. Gowers -- Curriculum Vitae for Endre Szemeredi / W.T. Gowers -- Abel and the Theory of Algebraic Equations / W.T. Gowers -- 1. Historical Context / Christian Skau -- 2. Correspondence with Legendre / Christian Skau -- 3. Addition Theorem / Christian Skau -- 4. Algebraic Equations-Primitive Elements / Christian Skau -- 5. Irreducibility Principle / Christian Skau -- 6. Galois Group / Christian Skau -- 7. Fundamental Theorem and Solvability Criterion / Christian Skau -- 8. Elliptic Functions and Algebraic Equations / Christian Skau -- 9. Transformation Theory and Teilingsgleichungen / Christian Skau -- 10. Posthumous Article / Christian Skau -- 11. Kronecker's Reaction / Christian Skau -- 12. Galois' Legacy / Christian Skau -- 13. Twists of Fate-Poetic Justice / Christian Skau -- 14. Abel-Galois Linkage / Christian Skau -- References / Christian Skau -- 2003 Jean-Pierre Serre / Christian Skau -- 2004 Sir Michael Atiyah and Isadore M. Singer / Christian Skau -- 2005 Peter D. Lax / Christian Skau -- 2006 Lennart Carleson / Christian Skau Summary Covering the years 2008-2012, this book profiles the life and work of recent winners of the Abel Prize: · John G. Thompson and Jacques Tits, 2008 · Mikhail Gromov, 2009 · John T. Tate Jr., 2010 · John W. Milnor, 2011 · Endre Szemerédi, 2012. The profiles feature autobiographical information as well as a description of each mathematician's work. In addition, each profile contains a complete bibliography, a curriculum vitae, as well as photos -- old and new. As an added feature, interviews with the Laureates are presented on an accompanying web site (http://extras.springer.com/). The book also presents a history of the Abel Prize written by the historian Kim Helsvig, and includes a facsimile of a letter from Niels Henrik Abel, which is transcribed, translated into English, and placed into historical perspective by Christian Skau. This book follows on The Abel Prize: 2003-2007, The First Five Years (Springer, 2010), which profiles the work of the first Abel Prize winners Subject Mathematics -- Awards. Computer science. Physics. Electronic Data Processing Physics physics. MATHEMATICS -- Essays. MATHEMATICS -- Pre-Calculus. MATHEMATICS -- Reference. Computer science Mathematics -- Awards Physics Form Electronic book Author Holden, H. (Helge), 1956- editor. Piene, Ragni, editor. ISBN 9783642394492 3642394493 3642394485 9783642394485

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