Establishes Lagrangian correspondences and 2(1-dim X)-shifted pretwistor structures on derived moduli stacks of perfect complexes with connections, compatible with Riemann-Hilbert and PTVV symplectic geometry.
O'Grady, Desingularized moduli spaces of sheaves on a K3 , J
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Proves a J-adapted Levi-Malcev decomposition for many 2-step solvable Lie algebras, confirming the Fino-Vezzoni conjecture for unimodular cases and characterizing SKT metrics on completely solvable ones.
Projective Kummer-type manifolds with finite-order symplectic birational self-maps acting nontrivially on H² are twisted modular except for Picard rank 3 cases characterized by their NS lattices; specific Mukai vectors are identified for finite-order wall-crossing maps on modular examples.
Classification of terminalizations of symplectic quotients of K3^{[n]} and generalized Kummer varieties yields at least nine new deformation types of irreducible symplectic varieties of dimension four.
Extends classification of rank-2 co-Higgs bundles on Hopf surfaces to construct Poisson 3-folds and describe their symplectic leaves.
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