Sep 8 , 3:30pm, Wean 8220

Oleg Pikhurko, CMU

Irrationality of the Turan Density

Oleg Pikhurko, CMU

Irrationality of the Turan Density

Abstract:

Let $\cal F$ be a family of $k$-graphs. The \emph{Tur\'an function
$ex(n,F)$} is the maximum number of edges in an $\cal F$-free
$k$-graph on $n$ vertices. The \emph{Tur\'an density $\pi(\cal F)$} is
the limit of $ex(n,F)/{n\choose k}$ as $n$ tends to infinity. (The
limit is known to exists for every $\cal F$.)

We disprove the conjecture of Chung and Graham that $\pi(\cal F)$ is rational for every finite family $\cal F$.