Proposes a CFT analogue of Hodge loci in Calabi-Yau sigma models via non-trivial TDL categories of topological defects, with CM number field embeddings at special points for elliptic curves and K3 surfaces.
Homological Algebra of Mirror Symmetry
8 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
This is my talk at ICM, Zurich 1994. It contains a short introduction, two basic examples and a refined version of the Mirror Conjecture formulated in terms of homological algebra.
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Authors define an Entropy flow on phase-parameter space that augments one-parameter vector field families with a parameter drift to realize transitions to chaos, and examine its behavior on standard routes and example systems.
Tropological sigma models on 4D targets are defined on filtered manifolds with nilpotent Engel algebra symmetries and conjectured to correspond to filtered Gromov-Witten invariants.
Ensemble averaging in holography is reframed as averaging over topological completions of a relative theory via SymTFT boundary conditions, reproducing known moments in Marolf-Maxfield and Narain models.
Proves Lagrangian correspondences in nonabelian Hodge theory for perfect complexes and establishes canonical shifted pretwistor structures on the Deligne-Hitchin-Simpson moduli stack over P^1_C.
Transpolar pairs involving VEX multitopes yield smooth toric spaces whose Chern classes satisfy Todd-Hirzebruch identities and belong to deformation families of generalized complete intersections.
Deformations in algebraic superstring models indicate a non-algebraic generalization that aligns with mirror duality requirements.
Generalizations beyond algebraic geometry in string theory remain aligned with mirror symmetry, support quantitative analysis, and point to deeper symplectic geometry connections.
citing papers explorer
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Hodge Loci and Complex Multiplication via Generalized Symmetries in Calabi-Yau sigma models
Proposes a CFT analogue of Hodge loci in Calabi-Yau sigma models via non-trivial TDL categories of topological defects, with CM number field embeddings at special points for elliptic curves and K3 surfaces.
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When Entropy flows: drifting along the route to Chaos
Authors define an Entropy flow on phase-parameter space that augments one-parameter vector field families with a parameter drift to realize transitions to chaos, and examine its behavior on standard routes and example systems.
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Nil-Equivariant Tropological Sigma Models on Filtered Geometries
Tropological sigma models on 4D targets are defined on filtered manifolds with nilpotent Engel algebra symmetries and conjectured to correspond to filtered Gromov-Witten invariants.
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From Baby Universes to Narain Moduli: Topological Boundary Averaging in SymTFTs
Ensemble averaging in holography is reframed as averaging over topological completions of a relative theory via SymTFT boundary conditions, reproducing known moments in Marolf-Maxfield and Narain models.
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Lagrangian correspondences of nonabelian Hodge type and shifted twistor structures
Proves Lagrangian correspondences in nonabelian Hodge theory for perfect complexes and establishes canonical shifted pretwistor structures on the Deligne-Hitchin-Simpson moduli stack over P^1_C.
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Chern Characteristics and Todd-Hirzebruch Identities for Transpolar Pairs of Toric Spaces
Transpolar pairs involving VEX multitopes yield smooth toric spaces whose Chern classes satisfy Todd-Hirzebruch identities and belong to deformation families of generalized complete intersections.
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Beyond Algebraic Superstring Compactification: Part II
Deformations in algebraic superstring models indicate a non-algebraic generalization that aligns with mirror duality requirements.
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Beyond Algebraic Solutions to Stringy Spacetime
Generalizations beyond algebraic geometry in string theory remain aligned with mirror symmetry, support quantitative analysis, and point to deeper symplectic geometry connections.