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Urban spatial structures from human flow by Hodge–Kodaira decomposition
Human flow in cities indicates social activity and can reveal urban spatial structures based on human behaviours for relevant applications. Scalar...
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Layered Hodge Decomposition for Urban Transit Networks
Modeling the amount of passenger flow along any given line segment of an urban transit network is a challenging task due to the complexity of the...
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Hodge similarities, algebraic classes, and Kuga–Satake varieties
We introduce in this paper the notion of Hodge similarities of transcendental lattices of hyperkähler manifolds and investigate the Hodge conjecture...
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Existence and density of typical Hodge loci
Motivated by a question of Baldi-Klingler-Ullmo, we provide a general sufficient criterion for the existence and analytic density of typical Hodge...
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Hodge numbers of O’Grady 6 via Ngô strings
We give an alternative computation of the Betti and Hodge numbers for manifolds of OG 6 type using the method of Ngô Strings introduced by de Cataldo,...
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Hodge theory of degenerations, (I): consequences of the decomposition theorem
We use the Decomposition Theorem to derive several generalizations of the Clemens–Schmid sequence, relating asymptotic Hodge theory of a degeneration...
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From Grassmann complements to Hodge-duality
Hodge duality is a central concept of 20th century algebraic and analytic geometry and plays a non-negligible role also in recent mathematical...
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Hodge theory-based biomolecular data analysis
Hodge theory reveals the deep intrinsic relations of differential forms and provides a bridge between differential geometry, algebraic topology, and...
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Hodge-Elliptic Genera, K3 Surfaces and Enumerative Geometry
K3 surfaces play a prominent role in string theory and algebraic geometry. The properties of their enumerative invariants have important consequences...
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FRÖLICHER SPECTRAL SEQUENCE AND HODGE STRUCTURES ON THE COHOMOLOGY OF COMPLEX PARALLELISABLE MANIFOLDS
For complex parallelisable manifolds Γ\ G , with G a solvable or semisimple complex Lie group, the Frölicher spectral sequence degenerates at the...
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Introduction to the Hodge Conjecture for Abelian Varieties
The original version of the conjecture was first formulated by Hodge in his 1950 ICM congress address [64]. In 1961 Atiyah and Hirzebruch formulated...
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The Ax–Schanuel conjecture for variations of mixed Hodge structures
We prove in this paper, the Ax–Schanuel conjecture for all admissible variations of mixed Hodge structures.
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Universal Equations for Higher Genus Gromov–Witten Invariants from Hodge Integrals
We establish new universal equations for higher genus Gromov–Witten invariants of target manifolds, by studying both the Chern character and Chern...
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Deformed WZW models and Hodge theory. Part I
We investigate a relationship between a particular class of two-dimensional integrable non-linear σ -models and variations of Hodge structures....
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The numerical Hodge standard conjecture for the square of a simple abelian variety of prime dimension
We prove the numerical Hodge standard conjecture for the square of a simple abelian variety of prime dimension, and also in some related cases.