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Erdös Centennial

  • Book
  • © 2013

Overview

Editors:
  1. László Lovász

    1. Department of Computer Science, Eötvös Lóránd University, Budapest, Hungary

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  2. Imre Z. Ruzsa

    1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary

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    You can also search for this editor in PubMed   Google Scholar

  3. Vera T. Sós

    1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary

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    You can also search for this editor in PubMed   Google Scholar

  • Published on the occasion of Paul Erdös 100th anniversary
  • This volume describes the way in which problems raised by Paul Erdös and topics initiated by him continue to flourish today
  • Contains contributions by outstanding researchers in these areas
  • The papers include extensive surveys of classical results as well as of new developments

Part of the book series: Bolyai Society Mathematical Studies (BSMS, volume 25)

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Table of contents (25 chapters)

  1. Front Matter

    Pages 1-10
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  2. Paul Erdős and Probabilistic Reasoning

    • Noga Alon
    Pages 11-33

  3. Euclidean vs. Graph Metric

    • Itai Benjamini
    Pages 35-57

  4. The Phase Transition in the Erdős-Rényi Random Graph Process

    • Béla Bollobás, Oliver Riordan
    Pages 59-110

  5. Around the Sum-product Phenomenon

    • Jean Bourgain
    Pages 111-128

  6. Small Doubling in Groups

    • Emmanuel Breuillard, Ben Green, Terence Tao
    Pages 129-151

  7. Erdős and Multiplicative Number Theory

    • Harold G. Diamond
    Pages 153-168

  8. The History of Degenerate (Bipartite) Extremal Graph Problems

    • Zoltán Füredi, Miklós Simonovits
    Pages 169-264

  9. Erdős and Arithmetic Progressions

    • W. Timothy Gowers
    Pages 265-287

  10. Paul Erdős and Egyptian Fractions

    • Ronald L. Graham
    Pages 289-309

  11. Perfect Powers in Products with Consecutive Terms from Arithmetic Progressions, II

    • Kálmán Győry
    Pages 311-324

  12. Erdős’s Work on Infinite Graphs

    • Péter Komjáth
    Pages 325-345

  13. The Impact of Paul Erdős on Set Theory

    • Kenneth Kunen
    Pages 347-363

  14. Some Problems and Ideas of Erdős in Analysis and Geometry

    • R. Daniel Mauldin
    Pages 365-376

  15. L 2 Majorant Principles

    • Hugh L. Montgomery
    Pages 377-381

  16. A Combinatorial Classic — Sparse Graphs with High Chromatic Number

    • Jaroslav Nešetřil
    Pages 383-407

  17. Small Ball Probability, Inverse Theorems, and Applications

    • Hoi H. Nguyen, Van H. Vu
    Pages 409-463

  18. The Beginnings of Geometric Graph Theory

    • János Pach
    Pages 465-484

  19. Paul Erdős and the Difference of Primes

    • János Pintz
    Pages 485-513

  20. Paul Erdős and the Rise of Statistical Thinking in Elementary Number Theory

    • Paul Pollack, Carl Pomerance
    Pages 515-533
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Keywords

About this book

Paul Erdös was one of the most influential mathematicians of the twentieth century, whose work in number theory, combinatorics, set theory, analysis, and other branches of mathematics has determined the development of large areas of these fields. In 1999, a conference was organized to survey his work, his contributions to mathematics, and the far-reaching impact of his work on many branches of mathematics. On the 100th anniversary of his birth, this volume undertakes the almost impossible task to describe the ways in which problems raised by him and topics initiated by him (indeed, whole branches of mathematics) continue to flourish. Written by outstanding researchers in these areas, these papers include extensive surveys of classical results as well as of new developments. 

Reviews

From the book reviews:

“Paul Erdős was a very influential mathematician. … The volume is an invaluable source for those students and researchers who are touched by Erdős’ mathematics.” (Péter Hajnal, Acta Scientiarum Mathematicarum (Szeged), Vol. 80 (1-2), 2014)

Editors and Affiliations

  • Department of Computer Science, Eötvös Lóránd University, Budapest, Hungary

    László Lovász

  • Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary

    Imre Z. Ruzsa, Vera T. Sós

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