=================================================================== ERDOS TALKS 2005 Endre Szemeredi =================================================================== Shalom all, This year's Erdos talks will be delivered by Endre Szemeredi, one of the most prominent combinatorists ever, whose work is greatly influenced by Erdos. The topics he has chosen for his talks are intended to reflect this to some extent. The first two talks will be delivered in the HUJI combinatorics and CS theory seminars in Jerusalem, and the third talk will be a plenary talk at the annual IMU meeting in Neve Ilan. Please find below the details: SECOND LECTURE Wednesday, May 18, 10:30-12:00, Math 110 "A hypergraph analogue of Dirac's theorem on Hamiltonian cycles." Talk 3: Thursday, May 19, 16:25-17:10, Neve Ilan "Some Erdös-type problems in combinatorial number theory." Abstracts: Talk 2: Dirac's theorem states that if in a graph G on n vertices the degree of every vertex is at least n/2 then the graph contains a Hamiltonian cycle. In a 3-uniform hypergraph H, the co-degree of two vertices x, y, denoted by d(x,y) is the number of vertices z such that {x,y,z} is an edge in H. We are going to prove that if d(x, y) is at least n/2 for every x and y, then H contains a Hamiltonian cycle, meaning a cyclical ordering of the vertices such that every three consecutive vertices form an edge. We will also prove the analogous statement for k-uniform hypergraphs with k>3. This is joint work with R. Rucinski and V. Rodl. Talk 3: In this talk we are going to discuss several problems concerning the size, density, or structure of sets of integers with certain properties. The approaches we use will combine ideas and tools from combinatorics, number theory, geometry, and harmonic analysis. Below is a list of some of the problems that we wish to address. a) Determine the minimum density of an infinite sequence of integers A = a1, a2, a3 ... for which the collection of finite subset sums of A contains an infinite arithmetic progression. b) For a finite set A and integer k, describe the structure of kA, the set of all sums of k distinct elements in A. c) For a finite set A, give a "good" bound on max {|A+A|, |AA|}, where A+A is the set of all sums of two elements in A and AA the set of all such products. d) For a finite set A, give a "good" bound on max |B| where B is a subset of A for which B+B is disjoint from A. This is joint work with B. Sudakov and V. H. Vu. --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel Announcement from: Ron Adin