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Dynamics lunch seminar: Jakub Konieczny (HUJI) "Monochromatic sums and products" | Einstein Institute of Mathematics

Dynamics lunch seminar: Jakub Konieczny (HUJI) "Monochromatic sums and products"

Date: 
Tue, 07/11/201712:00-13:00
Location: 
Manchester faculty lounge
Abstract:
A classical theorem of Schur asserts that whenever the positive integers are finitely coloured, we can find x and y such that x, y and x+y are monochromatic. A moment's thought suffices to see that the same statement holds for the pattern x, y, xy. What about the common generalisation, the pattern x, y, x+y, xy? Although this question was posed no later than 1979, the answer was not known until recently even for the much simpler pattern x+y, xy. In the paper of Moreira which will be the basis of my talk, the author shows that for any finite colouring of the positive integers, there exists a monochromatic pattern x, x+y, xy. The proof, as befits this seminar, relies on dynamics.