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Title An irregular mind : Szemerédi is 70 / Imre Bárány, József Solymosi (eds.)
Published Berlin : Springer ; Budapest : János Bolyai Mathematical Society, 2010
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Description 1 online resource (758 pages) : illustrations
Series Bolyai Society mathematical studies, 1217-4696 ; 21
Bolyai Society mathematical studies ; 21
Contents Cover13; -- Table of Contents -- Foreword -- List Of Publications Of Endre Szemeredi -- Universality, Tolerance, Chaos And Order -- 1. Introduction -- 2. The Strong Chromatic Number And Universal Graphs -- 3. Random Universal Fault Tolerant Graphs -- 4. Universal Graphs And Products Of Expanders -- 4.1. A Graph-Decomposition Result -- 4.2. A Sketch of the Universality of Gk, N -- 5. A Ramsey Type Problem -- 6. Balanced Homomorphisms And Subgraph Containment Problems -- 7. Concluding Remarks And Open Problems -- References -- Super-Uniformity Of The Typical Billiard Path -- 1. What Is Super-Uniformity? -- 1. Introduction. -- 2. Super-Uniformity of the Typical Billiard Path in the Unit Square. -- 2. Can We Beat The Monte Carlo Method? (I) -- 3. Can We Beat The Monte Carlo Method? (II) -- 1. Regular Sampling Is Adaptive. -- 2. A Surprising Way to "Beat" the Monte Carlo Method: Switching From Point Samples to Curves, Surfaces, and So on. -- 3. Summary. -- 4. Super-Uniformity: Proof Of Theorem 1 -- 5. Proof Of Theorem 2 -- 6. Proof Of Theorem 3 -- 7. Proof Of Theorem 4 -- 8. Proof Of Proposition 1.1 -- 9. Proof Of Proposition 2.1 -- 10. Proof Of Proposition 2.2 -- 11. Proof Of Proposition 3.1 -- 12. More On Super-Uniformity: Proof Of Theorem 5 -- References -- Percolation On Self-Dual Polygon Configurations -- 1. Introduction -- 2. The Model And Results -- 3. A Generalization Of Harris'S Lemma -- 3.1. High Probability Unions of Upsets -- 4. Colourings, Hypergraphs And Crossings -- 4.1. How Crossing Probabilities Vary -- 5. A Rectangle-Crossing Lemma -- 5.1. Bond Percolation on 7I} -- 5.2. A Rectangle-Crossing Lemma for Hyperlattices -- 5.3. A Stronger Rectangle-Crossing Lemma -- 6. Self-Duality And Rectangle Crossings -- 7. From Rectangle Crossings To Percolation -- 8. On The Critical Surface -- References -- On Exponential Sums In Finite Fields -- O. Introduction -- 1. A Sum-Product Property -- 2. Preliminary Estimates (1) -- 3. Preliminary Estimates (2) -- 4. Further Assumptions -- 5. Preliminary Estimates (3) -- 6. Estimation Of Trilinear Sums -- 7. Convolution Of Product Densities -- 8. The General Case -- References -- An Estimate Of Incomplete Mixed Character Sums -- Notation And Convention -- References -- Crossings Between Curves With Many Tangencies -- 1. Introduction -- 2. Levels -- Proof Of Theorem 1 -- 3. Constructive Upper Bound -- Proof Of Theorem 2 -- 4. Concluding Remarks -- References -- An Arithmetic Regularity Lemma, An Associated Counting Lemma, And Applications -- 1. Introduction -- 2. Proof Of The Arithmetic Regularity Lemma -- 3. Proof Of The Counting Lemma -- 4. Generalised Von Neumann Type Theorems -- 5. On A Conjecture Of Bergelson, Host, And Kra -- 6. Proof Of Szemeredi'S Theorem -- Appendix A. Properties Of Polynomial Sequences -- Appendix B.A Multiparameter Equidistribution Result -- Appendix C. The Baker-Campbell-Hausdorff Formula -- References -- Yet Another Proof Of Szemeredi's Theorem -- 1. I Ntroduction -- 2. Nilsequenc
Summary Szemerédi's influence on today's mathematics, especially in combinatorics, additive number theory, and theoretical computer science, is enormous. This volume is a celebration of Szemerédi's achievements and personality, on the occasion of his seventieth birthday. It exemplifies his extraordinary vision and unique way of thinking. A number of colleagues and friends, all top authorities in their fields, have contributed their latest research papers to this volume. The topics include extension and applications of the regularity lemma, the existence of k-term arithmetic progressions in various subsets of the integers, extremal problems in hypergraphs theory, and random graphs, all of them beautiful, Szemerédi type mathematics. It also contains published accounts of the first two, very original and highly successful Polymath projects, one led by Tim Gowers and the other by¡ Terry Tao
Bibliography Includes bibliographical references
Notes Print version record
Subject Szemerédi, E. -- Bibliography.
Combinatorial analysis.
Number theory.
Graph theory.
Genre/Form Bibliography.
Festschriften.
Bibliographies.
Form Electronic book
Author Szemerédi, E.
Bárány, Imre.
Solymosi, Jozsef, 1959-
Bolyai János Matematikai Társulat.
LC no. 2010930377
ISBN 1283076276
3642144446 (electronic bk.)
9781283076272
9783642144448 (electronic bk.)