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SUMMARY:Euclidean Ramsey sets and the block sets conjecture  - Maria Ivan 
 (Stanford)
DTSTART:20251120T143000Z
DTEND:20251120T153000Z
UID:TALK240670@talks.cam.ac.uk
CONTACT:103978
DESCRIPTION:A set X is called Euclidean Ramsey if\, for any k and sufficie
 ntly large m\, any k-colouring of R^m contains a monochromatic congruent c
 opy of X. This notion was introduced by Erdos\, Graham\, Montgomery\, Roth
 schild\, Spencer and Straus. They asked if a set is Ramsey if and only if 
 it is spherical\, meaning that it lies on the surface of a sphere. It is n
 ot too difficult to show that if a set is not spherical\, then it is not E
 uclidean Ramsey either\, but the converse is very much open despite extens
 ive research over the years. On the other hand\, the block sets conjecture
  is a purely combinatorial\, Hales-Jewett type of statement. It was introd
 uced in 2010 by Leader\, Russell and Walters. If true\, the block sets con
 jecture would imply that every transitive set (a set whose symmetry group 
 acts transitively) is Euclidean Ramsey. Similarly to the first question\, 
 the block sets conjecture remains very elusive. In this talk we discuss re
 cent developments on the block sets conjecture and their implications to E
 uclidean Ramsey sets.\nJoint work with Imre Leader and Mark Walters
LOCATION:MR12
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