Related papers: Classification of horizontal SL(2)'s

We associate to a multiple polylogarithm a holomorphic 1-form on the universal abelian cover of its domain. We relate the 1-forms to the symbol and variation matrix and show that the 1-forms naturally define a lift of the variation of mixed…

We develop a framework that systematically casts the solvability and uniqueness conditions of linearized geometric boundary-value problems into cohomological terms. The theory is designed to be applicable without assumptions on the…

In the recent works of a number of people there has emerged a beautiful new perspective on the arithmetic properties of Hodge structures. A central result in that development appears in a paper by Baldi, Klingler, and Ullmo. In this…

We study a class of evolutionary partial differential systems with two components related to second order (in time) non-evolutionary equations of odd order in spatial variable. We develop the formal diagonalisation method in symbolic…

We extend the relative theory of admissible pairs and $p$-adic Hodge structures introduced in Part II to allow variation in the underlying local systems of $\mathbb{Q}_p$-vector spaces and isocrystals. This extension accommodates, in…

This is a review article discussing the de Rham cohomology of period domains of Hodge structures. We explain it as the de Rham cohomology of differentiable stacks as of a moduli space. We also discuss the cohomology of the partial toroidal…

We introduce and study the category of Hodge microsheaves which is a Hodge-version of the category of microsheaves for a certain class of holomorphic exact symplectic manifolds. We then study Hodge-theoretic version of wrapped sheaves and…

For a particular class of pseudo manifolds, we show that the intersection cohomology groups for any perversity may be naturally represented by extended weighted $L^2$ harmonic forms for a complete metric on the regular stratum with respect…

In this paper, we will provide constructions of D-module structures on the complex computing the periodic cyclic homology of a stable infinity-category defined over a scheme of characteristic zero. We give two methods. The first one is…

We use tools from generalized complex geometry to develop the theory of SKT (a.k.a. pluriclosed Hermitian) manifolds and more generally manifolds with special holonomy with respect to a metric connection with closed skew-symmetric torsion.…

At the end of the 70s, Gross and Deligne conjectured that periods of geometric Hodge structures with multiplication by an abelian number field are products of values of the gamma function at rational arguments, with exponents determined by…

This article constructs Von Neumann invariants for constructible complexes and coherent D-modules on compact complex manifolds, generalizing the work of the author on coherent L 2-cohomology. We formulate a conjectural generalization of…

Let $f:\mathbb{C}^{n+1} \to \mathbb{C}$ be a germ of hypersurface with isolated singularity. One can associate to $f$ a polarized variation of mixed Hodge structure $\mathcal{H}$ over the punctured disc, where the Hodge filtration is the…

We construct toroidal partial compactifications of the moduli spaces of mixed Hodge structures with polarized graded quotients. They are moduli spaces of log mixed Hodge structures with polarized graded quotients. We construct them as the…

In this paper we are interested in proving that the infinitesimal variations of Hodge structure of hypersurfaces of high enough degree lie in a proper subvariety of the variety of all infinitesimal variations. This is proved using a space…

The category of rational mixed Hodge-Tate structures is a mixed Tate category. So thanks to the Tannakian formalism, it is equivalent to the category of finite dimensional graded comodules over a graded commutative Hopf algebra H over Q.…

We equip the odd nilHecke algebra and its associated thick calculus category with digrammatically local differentials. The resulting differential graded Grothendieck groups are isomorphic to two different forms of the positive part of…

Two dimensional classical integrable systems and different integrable deformations for them are derived from phase space realizations of classical $sl(2)$ Poisson coalgebras and their $q-$deformed analogues. Generalizations of Morse,…

Using the developed deformation theory on moduli spaces of quadratic differentials we derive variational formulas for objects associated with generalized $SL(2)$ Hitchin's spectral covers: Prym matrix, Prym bidifferential, Hodge and Prym…

The non-abelian Hodge correspondence maps a polystable $\mathrm{SL}(2,\mathbb{R})$-Higgs bundle on a compact Riemann surface $X$ of genus $g\geq2$ to a connection which, in some cases, is the holonomy of a branched hyperbolic structure. On…