Erdös Centennial

Contents.- Preface.- Alon, N.: Paul Erdös and Probabilistic Reasoning.- Benjamini, I.: Euclidean vs. Graph Metric.- Bollobas, B. and Riordan, O.: The Phase Transition in the Erdös–Rényi Random Graph Process.- Bourgain, J.: Around the Sum-product Phenomenon.- Breuillard, E., Green, B. and Tao, T.: Small Doubling in Groups.- Diamond, H. G.: Erdös and Multiplicative Number Theory.- Füredi, Z. and Simonovits, M.: The History of Degenerate (Bipartite) Extremal Graph Problems.- Gowers, W. T.: Erdös and Arithmetic Progressions.- Graham, R. L.: Paul Erdös and Egyptian Fractions.- Györy, K.: Perfect Powers in Products with Consecutive Terms from Arithmetic Progressions.- Komjáth, P.: Erdös’s Work on Infinite Graphs.- Kunen, K.: The Impact of Paul Erd˝os on Set Theory.- Mauldin, R. D.: Some Problems and Ideas of Erdös in Analysis and Geometry.- Montgomery, H. L.:
L
2 Majorant Principles.- Nesetril, J.: A Combinatorial Classic – Sparse Graphs with High Chromatic Number.- Nguyen, H. H. and Vu, V. H.: Small Ball Probability, Inverse Theorems, and Applications.- Pach, J.: The Beginnings of Geometric Graph Theory.- Pintz, J.: Paul Erdös and the Difference of Primes.- Pollack, P. and Pomerance, C.: Paul Erdös and the Rise of Statistical Thinking in Elementary Number Theory.- Rödl, V. and Schacht, M.: Extremal Results in Random Graphs.-Schinzel, A.: Erdös’s Work on the Sum of Divisors Function and on Euler’s Function.- Shalev, A.: Some Results and Problems in the Theory of Word Maps.- Tenenbaum, G.: Some of Erdös’ Unconventional Problems in Number Theory, Thirty-four Years Later.- Totik, V.: Erdös on Polynomials.- Vertesi, P.: Paul Erdös and Interpolation: Problems, Results, New Developments.