Related papers: Some open problems on holomorphic foliation theory
To a singular foliation on the plane corresponds a circular boundary at infinity endowed with a pre-lamination on the circle. We solve the converse direction. We determine which pre-lamination on the circle are boundary at infinity of a…
Two dimensional conformal field theories with large central charge and a sparse low-lying spectrum are expected to admit a classical string holographic dual. We construct a large class of such theories employing permutation orbifold…
Some recent results and problems in the theory of particles containing heavy quarks ar reviewed.
In the following, we will review the fundamental problem that prevents a complete understanding of a theory of supersymmetrical field representations and describe its possible relation to a similar problem facing superstring/M-theory.
We present several aspects of the "topology of meromorphic functions", which we conceive as a general theory which includes the topology of holomorphic functions, the topology of pencils on quasi-projective spaces and the topology of…
In this paper we study (smooth and holomorphic) foliations which are invariant under transverse actions of Lie groups.
When is a manifold a leaf of a complete closed foliation on the open unit ball? We give some answers to this question.
In this article we study deformations of a holomorphic foliation with a generic non-rational first integral in the complex plane. We consider two vanishing cycles in a regular fiber of the first integral with a non-zero self intersection…
I describe recent challenges in hierarchical galaxy formation theory, including the formation of disk galaxies and of ellipticals. Problems with cold dark matter are summarized, and possible solutions are presented. I conclude with a…
We investigate the existence, and lack of unicity, of a holomorphic fibration by discs transversal to a rational curve in a complex surface.
Despite much recent theoretical and observational progress in our knowledge of the early universe, many fundamental questions remain only partially answered. Here, we review the latest achievements and persisting problems in the…
In this article, we discuss some properties of holomorphic fibrations in the complex analytic setting.
Let f : Y -> X be a morphism of complex projective manifolds, and let F be a subsheaf of the tangent bundle which is closed under the Lie bracket, but not necessarily a foliation. This short paper contains an elementary and very geometric…
The study of the recently constructed group foliation for the geopotential forecast equation is continued. The group foliation consists of two systems, namely the automorphic and resolving systems, the analysis of which facilitates the…
The theory of Topological Modular Forms suggests the existence of deformation invariants for two-dimensional supersymmetric field theories that are more refined than the standard elliptic genus. In this note we give a physical definition of…
We study holomorphic foliations on normal crossings varieties arising as semistable degenerations. We do so by we exploring the notion of foliated d-semistability using the language of logarithmic structures in the sense of…
This survey paper addresses uniqueness questions for symplectic forms on closed manifolds, explains what is known in several examples, and reviews some open problems.
We study deformations of complex projective varieties that are homotopically or homologically trivial. We formulate several conjectures and give some examples and partial answers.
An important result for regular foliations is their formal semi-local triviality near simply connected leaves. We extend this result to singular foliations for all 2-connected leaves and a wide class of 1- connected leaves by proving a…
This article, written for undergraduate mathematics students, provides an accessible introduction to a few key problems in tiling theory: Heesch's problem, the isohedral number problem, and the existence of an aperiodic monotile. I…