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.
Author(s): Noga Alon (auth.), Imre Bárány, József Solymosi, Gábor Sági (eds.)
Series: Bolyai Society Mathematical Studies 21
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2010
Language: English
Pages: 758
Tags: Combinatorics; Field Theory and Polynomials
Front Matter....Pages 1-20
Universality, Tolerance, Chaos and Order....Pages 21-37
Super-Uniformity of The Typical Billiard Path....Pages 39-129
Percolation on Self-Dual Polygon Configurations....Pages 131-217
On Exponential Sums in Finite Fields....Pages 219-242
An Estimate of Incomplete Mixed Character Sums....Pages 243-250
Crossings Between Curves With Many Tangencies....Pages 251-260
An Arithmetic Regularity Lemma, An Associated Counting Lemma, and Applications....Pages 261-334
Yet Another Proof Of Szemerédi's Theorem....Pages 335-342
Online Linear Discrepancy of Partially Ordered Sets....Pages 343-357
On The Triangle Removal Lemma For Subgraphs of Sparse Pseudorandom Graphs....Pages 359-404
Almost All F-Free Graphs Have The Erdös-Hajnal Property....Pages 405-414
Regularity Partitions and The Topology of Graphons....Pages 415-446
Extremal Problems for Sparse Graphs....Pages 447-490
Squares In Sumsets....Pages 491-524
Are There Arbitrarily Long Arithmetic Progressions In The Sequence of Twin Primes?....Pages 525-559
Dirac-Type Questions For Hypergraphs — A Survey (Or More Problems For Endre To Solve)....Pages 561-590
Towards A Noncommutative Plünnecke-Type Inequality....Pages 591-605
Quasirandom Multitype Graphs....Pages 607-617
Pseudorandomness In Computer Science and In Additive Combinatorics....Pages 619-650
Introduction To The Polymath Project and “Density Hales-Jewett and Moser Numbers”....Pages 651-657
Polymath and The Density Hales-Jewett Theorem....Pages 659-687
Density Hales-Jewett and Moser Numbers....Pages 689-753
My Early Encounters With Szemerédi....Pages 755-758
