Joseph Palmer (University of Antwerp) will speak in the geometry seminar on Tuesday 17 March 2020 at 11h am in the Salle des Profs. Joseph’s title and abstract are to be announced.

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.

Daniel Waldram (Imperial College) will speak in the geometry seminar on Tuesday 28 April 2020 at 11h am in the Salle des Profs. Daniel’s title and abstract are to be announced.

Daniel Greb (Universität Duisburg-Essen) will speak in the geometry seminar on Tuesday 17 March 2020 at 11h am in the Salle des Profs. Daniel’s title is Projectively flat sheaves and characterisations of finite quotients of projective spaces and his abstract is below.

I will explain how to extend the classical characterisation of projective space among Kähler-Einstein Fano manifolds in terms of a Chern class (in)equality to the class of Fano varieties with Kawamata log terminal singularities. I will spend significant time on discussing the necessary tools, which range from analysis (harmonic metrics / Simpson correspondence) and classical differential geometry to algebraic geometry (local fundamental groups of klt singularities). This is joint work with Stefan Kebekus and Thomas Peternell, and partly with Behrouz Taji.