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.
Iterated spans and classical topological field theories
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abstract
We construct higher categories of iterated spans, possibly equipped with extra structure in the form of "local systems", and classify their fully dualizable objects. By the Cobordism Hypothesis, these give rise to framed topological quantum field theories, which are the framed versions of the "classical" TQFTs considered in the quantization programme of Freed-Hopkins-Lurie-Teleman. Using this machinery, we also construct an infinity-category of Lagrangian correspondences between symplectic derived algebraic stacks and show that all its objects are fully dualizable.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
Reviews homotopies in geometric BV formalism and builds new examples from RG flow and gauge changes to produce spans of quantum master actions with isomorphic effective actions.
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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.