Between geometry and combinatorics: the solution of an open problem on Schubert varieties

Schubert varieties have been introduced in the 19th century to solve problems in enumerative geometry. These well-known varieties are indexed by permutations and many of their properties can be expressed combinatorially in terms of permutations. As a further example of this interplay between geometry and combinatorics, a solution of a long open problem will be presented, namely the determination of the singular locus of a Schubert variety.