An Irregular Mind: Szemerédi is 70

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Imre Bárány, Jozsef Solymosi
Springer Science & Business Media, Feb 11, 2011 - Mathematics - 758 pages
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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.
 

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Contents

FOREWORD
7
LIST OF PUBLICATIONS OF ENDRE SZEMEREDI
9
UNIVERSALITY TOLERANCE CHAOS AND ORDER
21
SUPERUNIFORMITY OF THE TYPICAL BILLIARD PATH
39
PERCOLATION ON SELFDuAL POLYGON CONFIGURATIONS
130
ON EXPONENTIAL SUMS IN FINITE FIELDS
219
AN ESTIMATE OF INCOMPLETE MIXED CHARACTER SUMS
243
CROSSINGS BETWEEN CURVES WITH MANY TANGENCIES
251
REGULARITY PARTITIONS AND THE TOPOLOGY OF GRAPHONS
415
EXTREMAL PROBLEMS FOR SPARSE GRAPHS
447
SQUARES IN SUMSETS
491
ARE THERE ARBITRARILY LONG ARITHMETIC PROGRESSIONS IN THE SEQUENCE OF TWIN PRIMES?
525
DIRACTYPE QUESTIONS FOR HYPERGRAPHS A SURVEY OR MORE PROBLEMS FOR ENDRE TO SOLVE
561
TOWARDS A NONCOMMUTATIVE PLUNNECKETYPE INEQUALITY
591
QUASIRANDOM MULTITYPE GRAPHS
606
PSEUDORANDOMNESS IN COMPUTER S CIENCE AND IN ADDITIVE COMBINATORICS
619

AN ARITHMETIC REGULARITY LEMMA AN ASSOCIATED COUNTING LEMMA AND ApPLICATIONS
261
YET ANOTHER PROOF OF SZEMEREDIS THEOREM
335
ONLINE LINEAR DISCREPANCY OF PARTIALLY ORDERED SETS
343
ON THE TRIANGLE R EMOVAL L EMMA FOR S UBGRAPHS OF SPARSE P SEUDORANDOM GRAPHS
358
ALMOST ALL HFREE GRAPHS HAVE THE ERDOSHAJNAL PROPERTY
405
INTRODUCTION TO THE POLYMATH PROJECT AND DENSITY HALESJEWETT AND MOSER NUMBERS
651
POLYMATH AND THE DENSITY HALESJEWETT THEOREM
658
DENSITY HALESJEWETT AND MOSER NUMBERS
689
MY EARLY ENCOUNTERS WITH SZEMEREDI
754
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