2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59594This is the writeup of a talk given at the European Congress of Mathematics, Barcelona. It considers Picard-Lefschetz theory from the Floer cohomology viewpoint.20 pages, LaTeX2e. TeXnical problem should now be fixed, so that the images will appear even if you download the .ps fileSymplectic GeometryAlgebraic GeometryVanishing cycles and mutationtext