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.
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2026 2verdicts
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Constructs semiorthogonal decompositions for derived categories on quasi-smooth derived algebraic stacks indexed by component lattices, with examples for moduli stacks of G-bundles, G-Higgs bundles, and G-local systems.
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Lagrangian correspondences of nonabelian Hodge type and shifted twistor structures
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.
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Semiorthogonal decompositions for stacks
Constructs semiorthogonal decompositions for derived categories on quasi-smooth derived algebraic stacks indexed by component lattices, with examples for moduli stacks of G-bundles, G-Higgs bundles, and G-local systems.