An Irregular Mind

1. Front Matter

   Pages 1-20

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2. Universality, Tolerance, Chaos and Order

   • Noga Alon

   Pages 21-37

3. Super-Uniformity of The Typical Billiard Path

   • József Beck

   Pages 39-129

4. Percolation on Self-Dual Polygon Configurations

   • Béla Bollobás, Oliver Riordan

   Pages 131-217

5. On Exponential Sums in Finite Fields

   • Jean Bourgain

   Pages 219-242

6. An Estimate of Incomplete Mixed Character Sums

   • Mei-Chu Chang

   Pages 243-250

7. Crossings Between Curves With Many Tangencies

   • Jacob Fox, Fabrizio Frati, János Pacht, Rom Pinchasi

   Pages 251-260

8. An Arithmetic Regularity Lemma, An Associated Counting Lemma, and Applications

   • Ben Green, Terence Tao

   Pages 261-334

9. Yet Another Proof Of Szemerédi's Theorem

   • Ben Green, Terence Tao

   Pages 335-342

10. Online Linear Discrepancy of Partially Ordered Sets

    • Mitchel T. Keller, Noah Streib, William T. Trotter

    Pages 343-357

11. On The Triangle Removal Lemma For Subgraphs of Sparse Pseudorandom Graphs

    • Yoshiharu Kohayakawa, VojtĚch RÖdlt, Mathias Schacht, Jozef Skokan

    Pages 359-404

12. Almost All F-Free Graphs Have The Erdös-Hajnal Property

    • Martin Loebl, Bruce Reed, Alex Scott, Andrew Thomason, Stéphan Thomassé

    Pages 405-414

13. Regularity Partitions and The Topology of Graphons

    • László Lovász, Balázs Szegedy

    Pages 415-446

14. Extremal Problems for Sparse Graphs

    • Jaroslav NeŠetŘil, Patrice Ossona De Mendez

    Pages 447-490

15. Squares In Sumsets

    • Hoi H. Nguyen, Van H. Vu

    Pages 491-524

16. Are There Arbitrarily Long Arithmetic Progressions In The Sequence of Twin Primes?

    • János Pintz

    Pages 525-559

17. Dirac-Type Questions For Hypergraphs — A Survey (Or More Problems For Endre To Solve)

    • Vojtech Rödl, Andrzej RuciŃski

    Pages 561-590

18. Towards A Noncommutative Plünnecke-Type Inequality

    • Imre Z. Ruzsa

    Pages 591-605

19. Quasirandom Multitype Graphs

    • Joel Spencer

    Pages 607-617

20. Pseudorandomness In Computer Science and In Additive Combinatorics

    • Luca Trevisan

    Pages 619-650

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.

• Graph
• Hypergraph
• Node
• Prime
• computer
• computer science
• finite field
• number theory

• Alfred Rènyi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary

  Imre Bárány, Gábor Sági

• Department of Mathematics, University of British Columbia, Vancouver, Canada

  József Solymosi

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