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4:00 pm Thursday, April 18, 2013 Colloquium: Combinatorial richness of multiplicatively large setsby Vitaly Bergelson (Ohio State) in HB 227- Many famous results of additive combinatorics deal with combinatorial richness of additively large sets in N = {1,2,...}. For example, the celebrated Szemeredi's theorem states that any subset of N which has positive upper density in N, contains arbitrarily long arithmetic progressions. One is naturally inclined to inquire whether there are interesting results pertaining to MULTIPLICATIVELY large sets in N. The goal of this talk is to introduce and juxtapose various notions of additive and multiplicative largeness and to discuss multiplicative analogs of Szemeredi's theorem and its extensions. As we will see, the methods of ergodic theory are well suited to tackle the problems which naturally arise in this context. In particular, we will show that multiplicatively large sets have a very rich combinatorial structure, both multiplicative and (somewhat surprisingly) additive. The talk is intended for a general audience.
Submitted by jtanis@rice.edu |