PDEs are strange, often impenetrable things, just proving that a solution exists represents a far from trivial task; and any piece of information, however small, can shed invaluable light on the problems they represent. Many techniques exist to help analyze and decode this information, and all find a place in modern mathematics: one such technique appeals to a property of some of the most fundamental objects in mathematics- graphs.

A graph is simply a set of points together with a description of which are joined, often supplemented with a direction in which such a connection is established. By their very nature they are simple, and thus inherently universal, computing the most simplistic properties of such objects gives way to a wealth of results about any system that shares their basic structure.

One such property: the maximal balanced equivalence relations of an oriented tree (that is, a graph with directions included and no closed loops), tells us much about any PDE system it represents, but is often not easy to calculate. This calculation, and specifically an algorithm to compute it in polynomial time is the work of our speaker. Come along to MS03 this thursday (7:30-9:00) as John Aldis elucidates the theory behind his work. Then we go pubwards.