Density Ramsey Type Results
| Speaker: | Jim Geelen |
|---|---|
| Affiliation: | University of Waterloo |
| Room: | Mathematics 3 (M3) 3103 |
Abstract:
In this talk we will present the density versions of the Hales--Jewett Theorem and the Carlson--Simpson Theorem. The Hales--Jewett Theorem is one of the most representing theorems in Ramsey theory (see \cite{HJ}). Its density version was first proved by H. Furstenberg and Y. Katznelson in 1991 using Ergodic Theory (see \cite{FK2}). However, since then, combinatorial proofs have been discovered (see \cite{Pol} and \cite{DKT3}). We will comment on these proofs. The Density Carlson--Simpson Theorem is an extension of the Density Hales-Jewett Theorem and concerns the space of the left variable words. The proofs of the above results required a new regularity method that led to a concentration inequality which we will present if time permits.
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\end{document}