János Barát: A counterexample to Stein's Equi-n-square Conjecture (paper of Pokrovskiy and Sudakov)

In 1975 Stein conjectured that in every $n\times n$ array filled with the numbers $1,…,n$ with every number occuring exactly $n$ times, there is a partial transversal of size $n−1$. 

In this talk we  present the recent paper of Pokrovskiy and Sudakov  which shows that this conjecture is false and construct such arrays without partial transverals of size $n-C\log(n)$.