Related papers: Nilpotent orbits of a generalization of Hodge stru…

Twistor forms are a natural generalization of conformal vector fields on Riemannian manifolds. They are defined as sections in the kernel of a conformally invariant first order differential operator. We study twistor forms on compact…

We investigate $\mathbb{C}^\times$-families of flat connections whose leading term is a nilpotent Higgs field. Examples of such families include real twistor lines and families arising from the conformal limit. We show that these families…

Under a non-torsion assumption on Heegner points, results of Kolyvagin describe the structure of Shafarevich-Tate groups of elliptic curves. In this paper we prove analogous results for ($p$-primary) Shafarevich-Tate groups associated with…

For a compact complex manifold, we introduce holomorphic foliations associated with certain abelian subgroups of the automorphism group. Such foliations are generalizations of holomorphic principal torus bundles. If there exists a…

A complex integrable system determines a family of complex tori over a Zariski-open and dense subset in its base. This family in turn yields an integral variation of Hodge structures of weight $\pm 1$. In this paper, we study the converse…

We study pairs of structures, such as the Poisson-Nijenhuis structures, on the tangent bundle of a manifold or, more generally, on a Lie algebroid or a Courant algebroid. These composite structures are defined by two of the following, a…

We give a geometric interpretation of sheaf cohomology for higher degrees n in terms of torsors on the member of degree d=n-1 in hypercoverings of type r=n-2, endowed with an additional data, the so-called rigidification. This generalizes…

We construct by geometric methods a noncommutative model E of the algebra of regular functions on the universal (2-fold) cover M of certain nilpotent coadjoint orbits O for a complex simple Lie algebra g. Here O is the dense orbit in the…

The orbits of the group B of upper-triangular matrices acting on 2-nilpotent complex matrices via conjugation are classified via oriented link patterns, generalizing A. Melnikov's classification of the B-orbits on upper-triangular such…

An $n$-tuple of operators $(V_1,...,V_n)$ acting on a Hilbert space $H$ is said to be isometric if the operator $[V_1\...\ V_n]:H^n\to H$ is an isometry. We prove a decomposition for an isometric tuple of operators that generalizes the…

We construct completely integrable systems on the dual of the Lie algebra of any compact Lie group $K$ with respect to the standard Lie-Poisson structure. These systems generalize key properties of Gelfand-Zeitlin systems: A) the pullback…

We consider complements of standard Seifert surfaces of special alternating links. On these handlebodies, we use Honda's method to enumerate those tight contact structures whose dividing sets are isotopic to the link, and find their number…

Let $G$ be an adjoint algebraic group of type $B$, $C$, or $D$ over an algebraically closed field of characteristic 2. We construct a Springer correspondence for the Lie algebra of $G$. In particular, for orthogonal Lie algebras in…

We show that the category of mixed Hodge complexes admits a Cartan-Eilenberg structure, a notion introduced in [GNPR10] leading to a good calculation of the homotopy category in terms of (co)fibrant objects. This result provides a…

We study Hecke algebras of groups acting on trees with respect to geometrically defined subgroups. In particular, we consider Hecke algebras of groups of automorphisms of locally finite trees with respect to vertex and edge stabilizers and…

The notion of a \emph{higher-order algebroid}, as introduced by J\'o\'zwikowski and Rotkiewicz in their work \emph{Higher-order analogs of Lie algebroids via vector bundle comorphisms} (SIGMA, 2018), generalizes the concepts of a…

A systematic way to organise the interesting periods of automorphic forms on a reductive group $G$ is via the theory of nilpotent orbits of $G$. On the other hand, it is known that the theta correspondence can be used effectively to relate…

We characterize Poisson and Jacobi structures by means of complete lifts of the corresponding tensors: the lifts have to be related to canonical structures by morphisms of corresponding vector bundles. Similar results hold for generalized…

Let $X$ be a compact manifold, $D$ a real elliptic operator on $X$, $G$ a Lie group, $P\to X$ a principal $G$-bundle, and ${\mathcal B}_P$ the infinite-dimensional moduli space of all connections $\nabla_P$ on $P$ modulo gauge, as a…

We introduce mixed twistor $D$-modules, and establish the fundamental functorial property. We also prove that they are described as the gluing of admissible variations of mixed twistor structure. In a sense, mixed twistor $D$-modules could…