Combinatorial Richness of Multiplicatively Large Sets

Friday, April 26, 2013 at 1:00pm to 1:45pm

Bronfman Science Center, 106 18 Hoxsey St, Williamstown, MA 01267, USA

Combinatorial Richness of Multiplicatively Large Sets

Prof. Vitaly Bergelson, Ohio State University

Mathematics and Statistics Department Faculty Seminar


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 (e.g.,  the even numbers have density 1/2 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 various notions of additive and multiplicative largeness and to discuss multiplicative analogs of Szemeredi's theorem and its extensions. 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.

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Mathematics & Statistics

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