### Partition and density regularity for diagonal systems of equations

Combinatorics Seminar

5th October 2021, 11:00 am – 12:00 pm

Fry Building, 2.04

A system of polynomial equations is called partition regular if every finite colouring of the positive integers produces monochromatic solutions to the system. A system is called density regular if it has solutions over every set of integers with positive upper density. A classical theorem of Rado characterises partition regularity for linear systems, whilst Szemerédi’s theorem classifies all density regular linear systems. In this talk, I will report on my recent work on classifying partition and density regularity for sufficiently non-singular systems of diagonal polynomial equations.

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