Related papers: Another Relation Between Approaches to the Schottk…

The present paper describes a relation between the quotient of the fundamental group of a smooth quasi-projective variety by its second commutator and the existence of maps to orbifold curves. It extends previously studied cases when the…

Using the concept of Jacobi-Lie group and Jacobi-Lie bialgebra, we generalize the definition of Poisson-Lie symmetry to Jacobi-Lie symmetry. In this regard, we generalize the concept of Poisson-Lie T-duality to Jacobi-Lie T-duality and…

We establish a relationship between a certain notion of covering complexity of a Riemannian spin manifold and positive lower bounds on its scalar curvature. This makes use of a pairing between quantitative operator $K$-theory and Lipschitz…

This paper is a survey on relations between secant identities and soliton equations and applications of soliton equations to problems of algebraic geometry, i.e., the Riemann-Schottky problem and its analogues. A short introduction into the…

In this article we investigate the relations between three kinds of vector fields with close connection to each other. A compact orientable manifold enables us to integrate over it, which is very different from noncompact manifolds, and…

We extend unbounded Kasparov theory to encompass conformal group and quantum group equivariance. This new framework allows us to treat conformal actions on both manifolds and noncommutative spaces. As examples, we present unbounded…

We develop direct and inverse scattering theory for Jacobi operators with steplike coefficients which are asymptotically close to different finite-gap quasi-periodic coefficients on different sides. We give a complete characterization of…

We give a covariant treatment of the quadratic differential identities satisfied by the P-functions on the Jacobian of smooth hyperelliptic curves of genera 1, 2 and 3.

We explicitly describe the Jacquet-Langlands correspondence at the level of modular forms. This gives a simpler and more flexible solution to Eichler's basis problem for general level than earlier work of Hijikata-Pizer-Shemanske for…

This is the author's PhD thesis. Two main sections address various aspects of mirror symmetry for compact Calabi-Yau threefolds and the roles that classically modular varieties play in string theory compactifications. The main results…

The geometrical representation of the path integral reduction Jacobian obtained in the problem of the path integral quantization of a scalar particle motion on a smooth compact Riemannian manifold with the given free isometric action of the…

We revisit the classical two-dimensional McKay correspondence in two respects: The first one, which is the main point of this work, is that we take into account of the multiplicative structure given by the orbifold product; second, instead…

Motivated by a possible connection between the $\mathrm{SU}(N)$ instanton knot Floer homology of Kronheimer and Mrowka and $\mathfrak{sl}(N)$ Khovanov-Rozansky homology, Lobb and Zentner recently introduced a moduli problem associated to…

A theorem by Mumford implies that every automorphic line bundle on a pure open Shimura variety, equipped with an invariant smooth metric, can be uniquely extended as a line bundle on a toroidal compactification of the variety, in such a way…

The aim of this paper is to define two link invariants satisfying cubic skein relations. In the hierarchy of polynomial invariants determined by explicit skein relations they are the next level of complexity after Jones, HOMFLY, Kauffman…

Jacobi fields of classical solutions of a Hamiltonian mechanical system are quantized in the framework of vertical-extended Hamiltonian formalism. Quantum Jacobi fields characterize quantum transitions between classical solutions.

A particular case of the Jacobian conjecture is considered and for small dimensional cases a computational approach is offered

In this paper a recursive algorithm is presented for evaluating multivariate Pad\'e approximants (of the rectangular type described in the work of Lutterodt) which is analogous to the Jacobi formula for univariate Pad\'e approximants. This…

The goal of this paper is to establish a complete Khintchine-Groshev type theorem in both homogeneous and inhomogeneous setting, on analytic nondegenerate manifolds over a local field of positive characteristic. The dual form of Diophantine…

We use correspondences to define a purely topological equivariant bivariant K-theory for spaces with a proper groupoid action. Our notion of correspondence differs slightly from that of Connes and Skandalis. We replace smooth K-oriented…