Department of Mathematical SciencesEvents People Colloquia and Seminars Conferences Centers Positions Areas of Research About the Department Alumni
Algorithms, Combinatorics and Optimization Seminar
University of Cambridge
Title: Partition regularity in the rationals
Abstract: A system of linear equations with integer coefficients is partition regular if, whenever the natural numbers are finitely coloured, it has a monochromatic solution. Rado gave a good characterisation of the finite partition regular systems, but even examples of infinite partition regular systems are hard to find.
I will describe a new family of infinite partition regular systems, and how it can be used to answer a long-standing open question: if a system of equations is partition regular over the rationals, must it also be partition regular over the natural numbers?
Joint work with Neil Hindman and Imre Leader.