Related papers: Hodge Theory for Linearized Boundary-Value Problem…

We introduce a new Hermitian metric on the cohomology ring of compact K\"ahlerian manifolds with a pair $(v,w)$ satisfying certain Hodge-Riemann relations. An Hermitian metric on the exterior algebra of the cotangent bundle is also defined…

An algebraic theory of dualities is developed based on the notion of bond algebras. It deals with classical and quantum dualities in a unified fashion explaining the precise connection between quantum dualities and the low temperature…

We adapt algorithms for resolving the singularities of complex algebraic varieties to prove that the natural map of homology theories from complex bordism to the bordism theory of complex derived orbifolds splits. In equivariant stable…

A class of elliptic-hyperbolic equations is placed in the context of a geometric variational theory, in which the change of type is viewed as a change in the character of an underlying metric. A fundamental example of a metric which changes…

We introduce a high-order spline geometric approach for the initial boundary value problem for Maxwell's equations. The method is geometric in the sense that it discretizes in structure preserving fashion the two de Rham sequences of…

Xu introduced a family of root-tree-diagram nilpotent Lie algebras of differential operators, in connection with evolution partial differential equations. We generalized his notion to more general oriented tree diagrams. These algebras are…

Local gauge theories are in a complicated relationship with boundaries. Whereas fixing the gauge can often shave off unwanted redundancies, the coupling of different bounded regions requires the use of gauge-variant elements. Therefore,…

This paper presents a gentle introduction to cohomology vanishing theorems, largely based on the paper work of Hongshan Li. It offers an insightful exploration of unitary local systems on complex manifolds, particularly focusing on their…

We define a new type of Hall algebras associated e.g. with quivers with polynomial potentials. The main difference with the conventional definition is that we use cohomology of the stack of representations instead of constructible sheaves…

We construct GLSM invariants for a general choice of stability in both the narrow and broad sector cases and prove they form a Cohomological Field Theory. This is obtained by forming the analogue of a virtual fundamental class which lives…

We prove a closed formula for integrals of the cotangent line classes against the top Chern class of the Hodge bundle on the moduli space of stable pointed curves. These integrals are computed via relations obtained from virtual…

The linearizability of differential equations was first considered by Lie for scalar second order semi-linear ordinary differential equations. Since then there has been considerable work done on the algebraic classification of linearizable…

Suppose that Y is a cyclic cover of projective space branched over a hyperplane arrangement D, and that U is the complement of the ramification locus in Y. The first theorem implies that the Beilinson-Hodge conjecture holds for U if certain…

We define the notion of a loop Hodge structure -- an infinite dimensional generalization of a Hodge structure -- and prove that a suitable variation of this object over a complex manifold is equivalent to the datum of a harmonic bundle.…

General relativity can describe various gravitational systems of astrophysical relevance, like black holes and neutron stars, or even strongly coupled systems through the holographic duality. The characteristic initial (boundary) value…

In this note we discuss an abstract framework for standard boundary value problems in divergence form with maximal monotone relations as "coefficients". A reformulation of the respective problems is constructed such that they turn out to be…

This article reports on the confluence of two streams of research, one emanating from the fields of numerical analysis and scientific computation, the other from topology and geometry. In it we consider the numerical discretization of…

A manifold with fibered cusp metrics $X$ can be considered as a geometrical generalization of locally symmetric spaces of $\mathbb{Q}$-rank one at infinity. We prove a Hodge-type theorem for this class of Riemannian manifolds, i.e. we find…

The main problem addressed in the paper is the Torelli problem for n-dimensional varieties of general type, more specifically for varieties with ample canonical bundle. It asks under which geometrical condition for a variety the period map…

Using Saito's theory of mixed Hodge modules, we study a generalization of Hellus-Schenzel's "cohomologically complete intersection" property. This property is equivalent to perversity of the shifted constant sheaf. We relate the generalized…