Erd¶s Centennial

Contents.- Preface.- Alon, N.: Paul Erd¶s and Probabilistic Reasoning.- Benjamini, I.: Euclidean vs. Graph Metric.- Bollobas, B. and Riordan, O.: The Phase Transition in the Erd¶s-R©nyi Random Graph Process.- Bourgain, J.: Around the Sum-product Phenomenon.- Breuillard, E., Green, B. and Tao, T.: Small Doubling in Groups.- Diamond, H. G.: Erd¶s and Multiplicative Number Theory.- F¼redi, Z. and Simonovits, M.: The History of Degenerate (Bipartite) Extremal Graph Problems.- Gowers, W. T.: Erd¶s and Arithmetic Progressions.- Graham, R. L.: Paul Erd¶s and Egyptian Fractions.- Gy¶ry, K.: Perfect Powers in Products with Consecutive Terms from Arithmetic Progressions.- Komj¡th, P.: Erd¶s's Work on Infinite Graphs.- Kunen, K.: The Impact of Paul ErdËos on Set Theory.- Mauldin, R. D.: Some Problems and Ideas of Erd¶s in Analysis and Geometry.- Montgomery, H. L.: L2 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 Erd¶s and the Difference of Primes.- Pollack, P. and Pomerance, C.: Paul Erd¶s and the Rise of Statistical Thinking in Elementary Number Theory.- R¶dl, V. and Schacht, M.: Extremal Results in Random Graphs.-Schinzel, A.: Erd¶s'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 Erd¶s' Unconventional Problems in Number Theory, Thirty-four Years Later.- Totik, V.: Erd¶s on Polynomials.- Vertesi, P.: Paul Erd¶s and Interpolation: Problems, Results, New Developments.