Yoshihiko Mitsumatsu (Chuo University, Tokyo) will speak in the geometry seminar on Tuesday 24 March 2020 at 14h in the Salle des Profs. There will be two geometry seminars that day. Yoshihiko’s title is *Lefschetz fibration on Milnor fibres of certain singularities* and his abstract is below. **Update 8/03: **Yoshihiko’s talk has been cancelled because of travel restrictions due to the ongoing pandemic of Covid-19.

*Recently we found that the Milnor fibre of cusp or simple elliptic singularities of complex 3-variables admits a Lefschetz fibration to a disk with general fibres 2-torus. As Milnor fibres with natural complex structure are Stein manifolds, our Lefschetz fibration is not holomorphic. The construction will be only roughly indicated. Rather I will explain the folllowing applications. This fact implies, for example, that the Lawson type foliations, a codimension 1 foliation which is obtained as a modification of the Milnor fibration of the singularity, admits a leafwise symplectic structures (a regular Poisson structure). Also Arnold’s strange duality between certain mordality 1 singularities has a deep relation with this Lefschetz fibration. This view point gives a smooth decomposition of a K3 surface into two Milnor fibres. This talk is based on a recent joint work with Naohiko Kasuya, Hiroki Kodama, and Atsuhide Mori.*