2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67557Some recent progress towards understanding the cohomology of moduli spaces of curves is described. Madsen and Weiss have given a proof of a generalisation of Mumford's conjecture on the stable cohomology of these moduli spaces M_g, and other contributors have made advances related to Faber's conjectures on the tautological ring of M_g.ICM talk; 18 pagesAlgebraic Geometry14H10; 14H15; 32G15; 55R40; 57R20text