Related papers: Fiber integration on the Demailly tower
The widespread adoption of machine learning and other matrix intensive computing algorithms has inspired renewed interest in analog optical computing, which has the potential to perform large-scale matrix multiplications with superior…
We study the cohomology of broken toric varieties via the derived push-forward of the constant sheaf to a complex of polytopes, proving a Deligne-type decomposition theorem, degeneration of the associated Leray-Serre spectral sequence, and…
Starting from a subinvariant positive definite kernel under a branching pullback, we attach to the resulting kernel tower a canonical electrical network on the word tree whose edge weights are the diagonal increments. This converts diagonal…
We study an analogue of fibrations of topological spaces with the homotopy lifting property in the setting of C*-algebra bundles. We then derive an analogue of the Leray-Serre spectral sequence to compute the K-theory of the fibration in…
We study the tiling of a two-dimensional region of the plane by $K$-cell one-dimensional tiles, or $K$-mers. Unlike previous studies, which typically allowed for one single value of $K$ or sometimes a small assortment of fixed values, here…
The effective interaction energy of a colloidal sphere in a suspension containing small amounts of non-ionic polymers and a flat glass surface has been measured and calculated using total internal reflection microscopy (TIRM) and a novel…
This mostly expository paper records some basic facts about towers of homotopy fiber sequences. We give a proof that a pairing of towers induces a pairing of associated spectral sequences, for towers of spaces and towers of spectra.
In this paper, we consider an obstruction-theoretical construction of characteristic classes of fiber bundles by simplicial method. We can get a certain obstruction class for a deformation of $C_\infty$-algebra models of fibers and a…
We present an elementary approach to local combinatorial formulae for the Euler class of a fiber-oriented triangulated spherical fiber bundle. The approach is based on sections averaging technique and very basic knowledge of simplicial…
For differential calculi on noncommutative algebras, we construct a twisted de Rham cohomology using flat connections on modules. This has properties similar, in some respects, to sheaf cohomology on topological spaces. We also discuss…
The cohomology theory known as Tmf, for "topological modular forms," is a universal object mapping out to elliptic cohomology theories, and its coefficient ring is closely connected to the classical ring of modular forms. We extend this to…
Functor lifting along a fibration is used for several different purposes in computer science. In the theory of coalgebras, it is used to define coinductive predicates, such as simulation preorder and bisimilarity. Codensity lifting is a…
We introduce a model for Hermitian holormorphic Deligne cohomology on a projective algebraic manifold which allows to incorporate singular hermitian structures along a normal crossing divisor. In the case of a projective curve, the…
Demailly showed that the Hodge conjecture is equivalent to the statement that any (p,p)-dimensional closed current with rational cohomology class can be approximated by linear combinations of integration currents associated to subvarieties,…
A recursive extension of the hybrid tetrahedron method for Brillouin-zone integration is proposed, allowing iterative tetrahedron refinement and significantly reducing the error from the linear tetrahedron method. The Brillouin-zone…
We develop a theory of Morse homology and cohomology with coefficients in a derived local system, for manifolds and also more generally for colimits of spaces that have the homotopy type of manifolds, with a view towards Floer theory. The…
The purpose of this paper is to exhibit a natural construction between complex geometry and symplectic geometry following the idea of mirror symmetry. Suppose we are given a family of pairs of 2-dimensional K\"ahler tori and stable…
The computation of feedback control using Dynamic Programming equation is a difficult task due the curse of dimensionality. The tree structure algorithm is one the methods introduced recently that mitigate this problem. The method computes…
We initiate the study of deformation theory in the context of derived and higher log geometry. After reconceptualizing the "exactification"-procedures in ordinary log geometry in terms of Quillen's approach to the cotangent complex, we…
The goal of this paper is to offer a new construction of the de Rham-Witt complex of smooth varieties over perfect fields of characteristic $p>0$. We introduce a category of cochain complexes equipped with an endomorphism $F$ of underlying…