Olivier Debarre Title: Some varieties with PSL(2,F_{11})-actions Abstract: Starting from an explicit EPW sextic with an effective action of PSL(2,F_{11}) found by Giovanni Mongardi in his thesis, we construct various varieties with effective actions of this finite simple group of order 660. This leads to constructions of further interesting varieties, such as explicit smooth irrational Gushel-Mukai threefolds and their 10-dimensional principally polarized intermediate Jacobians. This is joint work with Giovanni Mongardi.