Related papers: Block Jacobi matrices, Barycentric limits and Mani…
We study the existence of geometrically controlled branched covering maps from $\mathbb R^3$ to open $3$-manifolds or to decomposition spaces $\mathbb S^3/G$, and from $\mathbb S^3/G$ to $\mathbb S^3$.
The geometry of rotations in dimensions 3, 4, and 5 is discussed using the matrix exponential map. Explicit closed formulas for the exponential of an antisymmetric matrix, as well as the logarithm of a rotation, are given for these…
After introducing some motivations for this survey, we describe a formalism to parametrize a wide class of algebraic structures occurring naturally in various problems of topology, geometry and mathematical physics. This allows us to define…
We use a generalization of the Gibbons-Hawking ansatz to study the behavior of certain non-compact Calabi-Yau manifolds in the large complex structure limit. This analysis provides an intermediate step toward proving the metric collapse…
This paper extends some results of Hatcher and Quinn beyond the metastable range. We give a bordism theoretic obstruction to deforming a map between manifolds simultaneously off of a collection of pairwise disjoint submanifolds under the…
We study certain moduli spaces of sheaves on Enriques surfaces thereby obtaining, in every odd dimension, new examples of Calabi-Yau manifolds. We describe the geometry (canonical bundle, fundamental group, second Betti number and certain…
We discuss the appearance of Jacobi automorphic forms in the theory of superconformal vertex algebras, explaining it by way of supercurves and formal geometry. We touch on related topics such as Ramanujan's differential equations for…
We study triples of graded rings defined over the deformation spaces for certain one-parameter families of Calabi-Yau threefolds. These rings are analogues of the rings of modular forms, quasi-modular forms and almost-holomorphic modular…
We provide a generalization of Bianchi's triply conjugate systems containing a family of deformations of 2-dimensional quadrics together with its B\"{a}cklund transformation to higher dimensions.
We study combinatorial problems related to the singularities and boundary components of toroidal compactifications of orthogonal modular varieties. In particular, those associated with the moduli of algebraic deformation generalised Kummer…
We collect some results and notions concerning generalizations for block Jacobi matrices of several concepts, which have been important for spectral studies of the simpler and better known scalar Jacobi case. We focus here on some issues…
We study complex networks formed by triangulations and higher-dimensional simplicial complexes representing closed evolving manifolds. In particular, for triangulations, the set of possible transformations of these networks is restricted by…
We prove that the set of parameters for which a virtual level appears at the edge of the continuous spectrum of a Jacobi matrix with a finite-rank diagonal perturbation constitutes an algebraic variety of codimension one. This variety…
The Tracy-Widom equations associated with level spacing distributions are realized as a special case of monodromy preserving deformations.
Branes and defects in topological Landau-Ginzburg models are described by matrix factorisations. We revisit the problem of deforming them and discuss various deformation methods as well as their relations. We have implemented these…
We give infinitely many new isomorphisms between moduli spaces of bundles on local surfaces and on local Calabi--Yau threefolds.
The class of three-diagonal Jacobi matrix with exponentially increasing elements is considered. Under some assumptions the matrix corresponds to unbounded self-adjoint operator in the weighted space. The weight depends on elements of the…
In this paper we have build the modified Hamiltonian formalism for geometric objects like the Jacobi fields and metric tensors. In this approach Jacobi fields and metric tensors are mapped among manifold. As an application, we have mapped a…
A selfadjoined block tridiagonal matrix with positive definite blocks on the off-diagonals is by definition a Jacobi matrix with matrix entries. Transfer matrix techniques are extended in order to develop a rotation number calculation for…
Masuda (2008) provided the characterization of real Bott manifolds in terms of three operations on upper triangular matrices. We provide a combinatorial characterization of real Bott manifolds up to diffeomorphism in terms of operations on…