OSU Math Seminar

2:30PM (in room MW 154)
Randall McCutcheon from the University of Memphis
Ergodic Theory and Probability Seminar
"IP_r -sets with polynomial weights and Szemeredi's theorem"

H. Furstenberg and Y. Katznelson proved the following extension
of Szemer\'edi's theorem on arithmetic progressions: given $\delta>0$
and $k\in {\bf N}$, there exist $r$ and $n$ having the property that for
any integers $u_1,\ldots ,u_r$ and any $E\subset \{ 1,2,\ldots ,N\max
|u_i|\}$ having relative density $\geq \delta$, $E$ contains an arithmetic progression
of length $k$ whose common difference is of the form $u_{i_1}+\cdots +
u_{i_l}$. Various possible polynomial versions of this result will be
formulated, at least one of which turns out to be true.

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It's all Ramsey theory, baby. Polynomialize the crap out of that *linear* function and take it up a few dimensions (literally and metaphorically).

I have to install LaTeX on the new computer still.