Speaker
Gabriela Laboska
University of Chicago
Talks at this conference:
Friday, 16:55, J336 
Some computabilitytheoretic aspects of partition regularity over rings 
A system of linear equations over a ring \(R\) is partition regular if for any finite coloring of \(R\), the system has a monochromatic solution. In 1933, Rado [3] showed that an inhomogeneous system is partition regular over \(\mathbb{Z}\) if and only if it has a constant solution. Following a similar approach, Byszewski and Krawczyk [1] showed that the result holds over any integral domain. In 2018, following a different approach, Leader and Russell [2] generalized this over any commutative ring \(R\). We analyze some of these combinatorial results from a computabilitytheoretic point of view, starting with a theorem by Straus [4] used in the work of [1] and [2] that generalizes an earlier result by Rado. Bibliography
