Benjamin Bakker (University of Illinois Chicago)
Georg Oberdieck (University of Bonn)
Giulia Saccà (Columbia University)
The notes are available below each talk.
The videos are available by clicking on the title of the talk (only last two talks).
3:00-3:45pm: Georg Oberdieck
Title: Fixed loci of holomorphic-symplectic varieties via equivariant categories
Abstract: If a symplectic automorphism of a moduli space of stable objects on a K3 surface is induced by a symplectic automorphism of the K3 surface, then it is not hard to describe its fixed locus. However, not all automorphisms are of this type. I will explain how to determine the fixed loci also in the more general case. The idea is to work with the corresponding categorical or 'non-commutative' quotient of the K3 surface. This leads to a moduli theoretic description of the fixed loci which holds in greater generality. Joint work with Thorsten Beckmann (Univ. of Bonn).
4:15-5:00pm: Giulia Saccà
Title: Fixed loci of anti-symplectic involutions
Abstract: In this talk I will present work with L. Flapan, E. Macrì, and K. O'Grady studying the geometry of fixed loci of anti-symplectic involutions on certain HK manifolds of K3^n type. It turns out that the geometry of these fixed loci depend on the lattice theoretic properties of the involutions considered and the two basic cases to keep in mind are that of the Lehn-Lehn-Sorger-van Straten 8fold and that of double EPW sextics.
5:30-6:15pm: Benjamin Bakker
Title: Recent developments in the moduli of singular symplectic varieties
Abstract: A recurring feature of hyperkähler manifolds is that their geometry is closely tied to the Hodge structure on their weight 2 cohomology. Verbitsky's global Torelli theorem, for instance, essentially shows that for any hyperkähler manifold, all deformations of the Hodge structure are realized geometrically exactly once, at least up to bimeromorphism. In this talk I will survey joint work with C. Lehn extending these moduli-theoretic results to the case of singular symplectic varieties, including a generalization of the global Torelli theorem. We will also discuss some more recent work with C. Lehn and H. Guenancia extending the decomposition of projective symplectic varieties by holonomy type due to Druel-Greb-Guenancia-Höring-Kebekus-Peternell to the nonprojective case.