Related papers: Examples of non-commutative Hodge structures

Multi-symplectic integrators are typically regarded as a discretization of the Hamiltonian partial differential equations. This is due to the fact that, for generic finite-dimensional Hamiltonian systems, there exists only one independent…

Hodge correlators are complex numbers given by certain integrals assigned to a smooth complex curve. We show that they are correlators of a Feynman integral, and describe the real mixed Hodge structure on the pronilpotent completion of the…

We develop a theory of noncommutative Poisson extensions. For an augmented dg algebra \(A\), we show that any shifted double Poisson bracket on \(A\) induces a graded Lie algebra structure on the reduced cyclic homology. Under the…

Let $X$ be a quasi-compact quasi-separated $p$-adic formal scheme that is smooth either over a perfectoid $\mathbb{Z}_p$-algebra or over some ring of integers of a $p$-adic field. We construct a fully faithful functor from perfect complexes…

Let $\k$ be a field, and let $A$ and $B$ be connected $\N$-graded $\k$-algebras. The algebra $A$ is said to be a graded right-free extension of $B$ provided there is a surjective graded algebra morphism $\pi: A \to B$ such that $\ker\pi$ is…

We show that plane bipolar posets (i.e., plane bipolar orientations with no transitive edge) and transversal structures can be set in correspondence to certain (weighted) models of quadrant walks, via suitable specializations of a bijection…

We consider arbitrary polarized variations of Hodge structure of weight two and $h^{2,0}=1$ over a non--singular complex algebraic curve $S$ and analyze the boundary behaviour of the associated Kudla--Millson theta series using Schmid's…

We classify topological phases of non-Hermitian systems in the Altland-Zirnbauer classes with an additional reflection symmetry in all dimensions. By mapping the non-Hermitian system into an enlarged Hermitian Hamiltonian with an enforced…

Structures based on polarities have been used to provide relational semantics for propositional logics that are modelled algebraically by non-distributive lattices with additional operators. This article develops a first order notion of…

A relational structure is indivisible if for every partition of its set of elements into two parts there exists an embedding of the structure into one of the parts of the partition. A relational structure is homogeneous if every embedding…

We prove that the coherent cohomology of a proper morphism of noetherian schemes can be made arbitrarily p-divisible by passage to proper covers (for a fixed prime p). Under some extra conditions, we also show that p-torsion can be killed…

Let A be the moduli space of (1,p)-polarised abelian surfaces with a level structure, for p an odd prime. Let X be a desingularisation of any algebraic compactification of A. Then X is simply-connected.

In this paper, we establish the sheafified version of the cohomological integrality conjecture for stacks obtained as a quotient of a smooth affine symmetric algebraic variety by a reductive algebraic group equipped with an invariant…

In this paper, we establish a structure theorem for connected graded Hopf algebras over a field of characteristic $0$ by claiming the existence of a family of homogeneous generators and a total order on the index set that satisfy some…

It is well known that the twisters, section of twister space, classify the almost complex structure on even dimensional Riemannian manifold $X$. In this paper, it will be proved that a harmonic and anti-holomorphic twister is equivalent ti…

We will introduce twisted cycles and their associated regulators to cohomology. We prove the conjecture that this regulator is surjective for a general smooth projective surface. We construct indecomposable twisted cycles on elliptic…

A compact solvmanifold of completely solvable type, i.e. a compact quotient of a completely solvable Lie group by a lattice, has a K\"ahler structure if and only if it is a complex torus. We show more in general that a compact solvmanifold…

Based on the Connes--Kreimer Hopf algebra of rooted trees, the rooted tree maps are defined as linear maps on noncommutative polynomial algebra in two indeterminates. It is known that they induce a large class of linear relations for…

Odd exact Courant algebroids constitute a simple class of transitive Courant algebroids. Their underlying vector bundle is of odd rank and differs from a generalized tangent bundle by the addition of a line bundle. In this article we study…

Non-Hermiticity significantly enriches the concepts of symmetry and topology in physics. Particularly, non-Hermiticity gives rise to the ramified symmetries, where the non-Hermitian Hamiltonian $H$ is transformed to $H^\dagger$. For…