Recent progress in the study of Latin squares

Abstract

A Latin square of order $n$ is an $n$ by $n$ grid filled with $n$ symbols so that each symbol appears exactly once in each row and each column. From their early origins in recreational mathematics, Latin squares have been formally studied for their combinatorial properties since the late 18th century. More recently, tools from extremal and probabilistic combinatorics have been applied to Latin squares to make progress on a range of old questions. This brief survey will concentrate on the topics covered by the author’s talk at the 9th European Congress of Mathematics, while highlighting recent relevant surveys in the area.