Seminar series
Date
Mon, 21 Oct 2024
16:00
16:00
Location
C3
Speaker
Matt Bowen
Organisation
University of Oxford
We show that any finite coloring of an amenable group contains 'many' monochromatic sets of the form $\{x,y,xy,yx\},$ and natural extensions with more variables. This gives the first combinatorial proof and extensions of Bergelson and McCutcheon's non-commutative Schur theorem. Our main new tool is the introduction of what we call `quasirandom colorings,' a condition that is automatically satisfied by colorings of quasirandom groups, and a reduction to this case.