Déploiement, Stratification, and Monodromy Group in Complex Hypersurface Singularities

Explore complex hypersurface singularities and their geometric monodromy groups in this 48-minute lecture by Norbert A'Campo from the Université de Bâle, presented at the Institut des Hautes Etudes Scientifiques (IHES). Delve into the computation methods for geometric monodromy groups, starting with the seminal example of the Pham spine in the Milnor fibre of a Pham singularity. Examine how this spine computes the symplectic local monodromy diffeomorphism as a generalized Dehn twist. Investigate the characterization of local monodromy diffeomorphisms for curve singularities on normal surfaces as mixed tête-à-tête diffeomorphisms. Learn about generating sets of monodromy mapping classes obtained through real morsification and their description as framed mapping class groups. Conclude with a presentation of a real analytic stratification of smooth fibres for An-type plane curve singularities, discussing monodromy through wall crossing data. Consider the proposed conjecture generalizing these concepts to all plane curve singularities based on recent research.