BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Benjamin Bakker\, Daniel Huybrechts\, Andrew Swann\, Claire Voisin DTSTART:20201103T064500Z DTEND:20201103T070000Z DTSTAMP:20260423T005819Z UID:tacos/6 DESCRIPTION:Title: Hy perkähler Geometry\nby Benjamin Bakker\, Daniel Huybrechts\, Andrew S wann\, Claire Voisin as part of Geometry and TACoS\n\n\nAbstract\n- Benjam in Bakker (University of Illinois at Chicago): "Towards a BBDGGHKP decompo sition theorem for nonprojective Calabi–Yau varieties"\n\nAbstract. Cala bi-Yau manifolds are built out of simple pieces by the Beauville–Bogomol ov decomposition theorem: any Calabi–Yau Kahler manifold up to an etale cover is a product of complex tori\, irreducible holomorphic symplectic ma nifolds\, and strict Calabi-Yau manifolds (which have no holomorphic forms except a holomorphic volume form). Work of Druel–Guenancia–Greb–Hor ing–Kebekus–Peternell over the last decade has culminated in a general ization of this result to projective Calabi–Yau varieties with the kinds of singularities that arise in the MMP\, and the proofs heavily use algeb raic methods. In this talk I will describe some work in progress with C. L ehn and H. Guenancia extending the decomposition theorem to nonprojective varieties via deformation theory. I will also discuss applications to the K-trivial case of a conjecture of Peternell asserting that any minimal Ka hler space can be approximated by algebraic varieties.\n\n- Daniel Huybrec hts (Universität Bonn): "3 families of K3 surfaces"\n\nAbstract. I will r eview three one-dimensional families of K3 surfaces (twistor\, Brauer or T ate-Shafarevich\, and Dwork) and explain how\, from a purely Hodge-theoret ic perspective\, they fit into one picture. I am particularly interested i n understanding how certain properties propagate along those families.\n\n - Andrew Swann (Aarhus University): "HyperKähler metrics and symmetries"\ n\nAbstract. HyperKähler metrics are surveyed and discussed from the poin t of view of Lie group symmetries\, so principally in the non-compact case . This includes the Gibbons-Hawking ansatz in dimension four\, cotangent b undles\, coadjoint orbits. A common theme is quotient constructions and va rious ideas related to symplectic reduction. Relations to other geometric structures naturally arise and show that metrics of indefinite signature h ave an important role.\n\n- Claire Voisin (Collège de France): "On the Le fschetz standard conjecture for hyper-Kähler manifolds"\n\nAbstract. The Lefschetz standard conjecture is of major importance in the theory of mot ives. It is open starting from degree 2 and in that degree\, it predicts t hat any holomorphic 2-form on a smooth projective manifold is induced from a 2-form on a surface by a correspondence. I will discuss some results an d further expectations in the hyper-Kähler setting.\n\nThe discussion is open at https://gitter.im/GTACOS-November2020/. The live discussion with t he speakers for this series of talks will be held on November 18\, see htt ps://researchseminars.org/talk/tacos/7/\n LOCATION:https://researchseminars.org/talk/tacos/6/ END:VEVENT END:VCALENDAR