  This paper proves the sunflower conjecture by confirming that a family
${\mathcal F}$ of sets each of cardinality at most $m$ includes a
$k$-sunflower, if $|{\mathcal F}| >[ ck \log (k+1)]^m$ for a constant $c>0$
independent of $m$ and $k$, where $k$-sunflower stands for a family of $k$
different sets with common pair-wise intersections.
