The Sunflower Conjecture Proven

Abstract: 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.