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Cohomology of holomorphic line bundles and Hodge symmetry on Oeljeklaus–Toma manifolds
We prove the Hodge symmetry type result on the Dolbeault cohomology of Oeljeklaus–Toma manifolds with values in the direct sum of holomorphic line...
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Mixed Hodge Structures Applied to Singularities
We give a survey of applications of mixed Hodge theory to the study of isolated singularities. A summary of mixed Hodge theory is followed by some...
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Supersymmetry and Hodge theory on Sasakian and Vaisman manifolds
Sasakian manifolds are odd-dimensional counterpart to Kähler manifolds. They can be defined as contact manifolds equipped with an invariant Kähler...
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Hodge decompositions for Lie algebroids on manifolds with boundary
We investigate when the Chevalley-Eilenberg differential of a complex Lie algebroid on a manifold with boundary admits a Hodge decomposition. We...
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Chen-Jiang decompositions for projective varieties, without Hodge modules
We give a new proof of a theorem by Pareschi, Popa and Schnell that the direct image of the canonical bundle of a smooth projective variety along a...
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Cohomology of semisimple local systems and the decomposition theorem
In this paper, we study the cohomology of semisimple local systems in the spirit of classical Hodge theory. On the one hand, we construct a...
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A Note on the Filtered Decomposition Theorem
We generalize the logarithmic decomposition theorem of Deligne–Illusie to a filtered version. There are two applications. The easier one provides a...
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Coupled Domain-Boundary Variational Formulations for Hodge–Helmholtz Operators
We couple the mixed variational problem for the generalized Hodge–Helmholtz or Hodge–Laplace equation posed on a bounded 3D Lipschitz domain with the...
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The Generalized Roof F(1, 2,n): Hodge Structures and Derived Categories
We consider generalized homogeneous roofs, i.e. quotients of simply connected, semisimple Lie groups by a parabolic subgroup, which admit two...
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Hodge conjecture for the moduli space of semi-stable sheaves over a nodal curve
In this article, we prove the Hodge conjecture for a desingularization of the moduli space of rank 2, semi-stable, torsion-free sheaves with fixed...
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Boundedness of H ∞ Functional Calculus of Hodge-Dirac Operators
In this chapter, we introduce Hodge-Dirac operators associated with markovian semigroups of Fourier multipliers and we show that these operators...
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The c-map as a functor on certain variations of Hodge structure
We give a new manifestly natural presentation of the supergravity c-map. We achieve this by giving a more explicit description of the correspondence...
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The Hodge star operator and the Beltrami equation
An essentially unique homeomorphic solution to the Beltrami equation with measurable coefficients was found in the 1930s by Morrey. The most...
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An Introduction to p-Adic Hodge Theory
These notes provide an introduction to p-adic Hodge theory. They are based on the series of lectures given by the author at the International Center...
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The non-abelian Hodge correspondence on some non-Kähler manifolds
The non-abelian Hodge correspondence was established by Corlette (1988), Donaldson (1987), Hitchin (1987) and Simpson (1988, 1992). It states that on...