22.11.29, Imre Leader, Euclidean Ramsey Theory

Описание: ECOPRO Online Workshop: Developments in Combinatorics
https://www.ibs.re.kr/ecopro/online-w...

Imre Leader, Euclidean Ramsey Theory
November 29 2022, Tuesday @ 5:40 PM - 6:20 PM KST
Zoom

SPEAKER
Imre Leader
University of Cambridge
https://www.maths.cam.ac.uk/person/ibl10

The famous conjecture of Erdos, Graham, Montgomery, Rothschild, Spencer and Straus is that a set is Ramsey if and only if it embeds in a sphere. Here as usual “Ramsey” means that for every k there is an n such that whenever we k-colour real n-dimensional space there is a copy of the set that is monochromatic. We propose a “rival” conjecture, that a set is Ramsey if and only if it embeds into a (finite) transitive set. We will discuss the motivation for this conjecture, as well as how it relates to the original conjecture.

(Joint work with Paul Russell and Mark Walters).