# Research Spotlight

PROJECT SPOTLIGHT |
Ramsey Theory is a cohesive sub-discipline of combinatorics. The theme of Ramsey Theory is that ‘complete chaos is impossible.’ Or, one could say that Ramsey Theory is ‘the study of unavoidable regularities in large structures.’ There are applications of Ramsey Theory to number theory, geometry, topology, set theory, logic, ergodic theory, information theory, and theoretical computer science. (A recent survey article on applications of Ramsey Theory has a bibliography of 252 items.) Two of the largest branches of Ramsey Theory start with either ‘Ramsey's Theorem’ on the one hand, or ‘van der Waerden's Theorem on Arithmetic Progressions’ on the other. These two branches sometimes overlap, but a great number of results can be placed on one branch or the other. A few examples of various problems in Ramsey theory that the IRMACS Ramsey Theory Working Group has been discussing, both new and longstanding, follow:
- Is it true that any sequence with at least four symbols, i.e., any
sequence a Quite recently the group was able to answer the longstanding question by Erdos and Graham if every linear ordering of the set of real numbers contains long monotone arithmetic progressions. Current Member Listing: Hayri Ardal, Tom Brown, and Veselin Jungic. |