### Euclidean Ramsey Theory

Combinatorics Seminar

15th December 2021, 11:00 am – 12:00 pm

Fry Building, 2.04

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.

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