Talks by Andrea Petracci (Università di Bologna) and Jonas Stelzig (Universität München).
Schedule
Recently Kähler-Einstein metrics (or more precisely their algebraic counterpart, which is called K-stability) have been spectacularly applied to construct projective moduli spaces of Fano varieties. In this talk, after giving necessary introduction, I will explain how to use toric singularities and their deformation theory to obtain singular points on K-moduli spaces of Fano varieties. This talk is partly based on joint work with Anne-Sophie Kaloghiros.
14:15-14:45 Coffee & cake
14:45-15:45 Pluripotential homotopy theory (J. Stelzig)
By results of Sullivan from the 70's, one may model (finite type, simply connected) spaces up to rational homotopy equivalence by their commutative differential graded algebras of (piecewise-linear) differential forms. For example, one may use this algebra to calculate the homotopy groups modulo torsion, or certain higher operations Massey products. Inspired by this, and recent constructions by Angella, Tomassini, Tardini, and Sferuzza, we discuss the following invariant of complex manifolds: the equivalence class of the bigraded, bidifferential algebra of $\mathbb{C}$-valued differential forms, modulo a notion of quasi-isomorphism that tracks information on existence and uniqueness of pluripotentials, i.e., the d-dbar-equation $x=\partial\bar\partial y$.
