Conference Description
The observation brings the methods of singularity theory to bear on the problem, since the Milnor fibre is one of the basic invariants of a singularity. Its (reduced) Euler characteristic or cohomology can be codified by the powerful language of nearby/vanishing cycles of constructible functions or sheaves. This point of view also allows for local 'motifications' and 'categorifications', respectively, where one replaces a numerical invariant (an Euler characteristic) by a motivic class or a Hodge theoretical cohomology group coming from the motivic class or mixed Hodge module of vanishing cycles. This point of view has inspired a great deal of recent activity in the field. A key technical result is a corresponding Thom-Sebastiani theorem for vanishing cycles.