Imre Leader

Euclidean Ramsey Theory

Euclidean Ramsey Theory is a natural multidimensional version of
Ramsey Theory. A subset of Euclidean space is called Ramsey if, for any k,
whenever we partition Euclidean space of sufficiently high dimension into
k classes, one class much contain a congruent copy of our subset. It is still
unknown which sets are Ramsey. We will present background, involving the
known results, and then put forward a new conjecture which is the first
`challenge' to the accepted main conjecture in the area.