Date
Mon, 19 Mar 1951 05:15 -
Mon, 28 Jun 1965 11:15
Location
Philippines
Speaker
Imre Leader
Organisation
Cambridge

We will examine how the various notions of partition regularity change as we change the ambient space. A typical question would be as follows. We say that the system of equations $Ax=b$, where $A$ is an integer matrix and $b$ is a (non-zero) integer vector, is partition regular if whenever the integers are finitely coloured there is a monochromatic vector $x$ with $Ax=b$. Rado proved that the system $Ax=b$ is partition regular if and only if it has a constant solution. What happens if the integers are replaced by the rationals, or the reals, or a more general ring? 


No previous knowledge of partition regularity is assumed. This is based on joint work with Paul Russell and joint work with Ben Barber, Neil Hindman and Dona Strauss.

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