Robert Berman: Polystability thresholds vs log canonical thresholds on Fano manifolds

Speaker
Robert Berman, Chalmers

Abstract
In this talk, I will introduce an algebraic invariant of a Fano manifold X – the Gibbs polystability threshold of X. The invariant leads to an effective sufficient criterion for the existence of a Kähler–Einstein metric on X, reducing the problem to the computation of finitely many log canonical thresholds; the criterion is also necessary if the conjectural equality holds. The motivation comes from a probabilistic approach to constructing Kähler–Einstein metrics. This is based on a joint work with Rolf Andreasson and Ludvig Svensson.