Related papers: Quasisymmetric sewing in rigged Teichmueller space

We give a description of the completion of the manifold of all smooth Riemannian metrics on a fixed smooth, closed, finite-dimensional, orientable manifold with respect to a natural metric called the $L^2$ metric. The primary motivation for…

Our goal is to describe superconformal structures on super Riemann surfaces (SRS), based on data assigned to a fatgraph. We start from the complex structures on punctured $(1|1)$-supermanifolds, characterizing the corresponding moduli and…

We give a parametrization to the asymptotic Teichmuller space of the open unit disk through equivalent classes of shear functions induced by quasisymmetric homeomorphisms on the Farey tesselation of the unit disk. Then using the…

We show that all lowest Landau level projected and unprojected chiral parton type fractional quantum Hall ground and edge state trial wave functions, which take the form of products of integer quantum Hall wave functions, can be expressed…

Two-dimensional conformal field theory (CFT) can be defined through its correlation functions. These must satisfy certain consistency conditions which arise from the cutting of world sheets along circles or intervals. The construction of a…

An almost Fuchsian 3-manifold is a quasi-Fuchsian manifold which contains an incompressible closed minimal surface with principal curvatures in the range of $(-1,1)$. Such a 3-manifold $M$ admits a foliation of parallel surfaces, whose…

We study moduli of semistable twisted sheaves on smooth proper morphisms of algebraic spaces. In the case of a relative curve or surface, we prove results on the structure of these spaces. For curves, they are essentially isomorphic to…

I describe a project to open a new territory of quantum field theory where the fields live not on a space-time manifold but on certain complete metric spaces of (n-1)-dimensional objects (defects) in a 2n-dimensional space-time M. These…

In a joint work with Saji, the second and the third authors gave an intrinsic formulation of wave fronts and proved a realization theorem of wave fronts in space forms. As an application, we show that the following four objects are…

In this article, we summarize the results on symmetric conformal geometries. We review the results following from the general theory of symmetric parabolic geometries and prove several new results for symmetric conformal geometries. In…

On the thick part of the moduli space of Riemann surfaces, where there is a positive lower bound of the systole of the surface, we show that all Weil-Petersson Riemannian curvatures are bounded, independent of the genus of the surface.

Donaldon constructed a hyperk\"ahler moduli space $\mathcal{M}$ associated to a closed oriented surface $\Sigma$ with $\textrm{genus}(\Sigma) \geq 2$. This embeds naturally into the cotangent bundle $T^*\mathcal{T}(\Sigma)$ of Teichm\"uller…

Boundaries not only are fundamental elements in nearly all realistic physical systems, but also greatly enrich the structure of quantum field theories. In this paper, we demonstrate that conformal field theory (CFT) with a boundary, known…

The classical uniformization theorem states that any simply connected Riemann surface is conformally equivalent to the disk, the plane, or the sphere, each equipped with a standard conformal structure. We give a similar uniformization for…

Given a closed surface endowed with a volume form, we equip the space of compatible Riemannian structures with the structure of an infinite-dimensional symplectic manifold. We show that the natural action of the group of volume-preserving…

We develop further the theory of Rational Conformal Field Theories (RCFTs) on a cylinder with specified boundary conditions emphasizing the role of a triplet of algebras: the Verlinde, graph fusion and Pasquier algebras. We show that…

In large part, the future utility of modern numerical conformal bootstrap depends on its ability to accurately predict the existence of hitherto unknown non-trivial conformal field theories (CFTs). Here we investigate the extent to which…

Harmonic maps from Riemann surfaces arise from a conformally invariant variational problem. Therefore, on one hand, they are intimately connected with moduli spaces of Riemann surfaces, and on the other hand, because the conformal group is…

In this article we give a survey of homology computations for moduli spaces $\mathfrak{M}_{g,1}^m$ of Riemann surfaces with genus $g\geqslant 0$, one boundary curve, and $m\geqslant 0$ punctures. While rationally and stably this question…

We define simple tilings in the general context of a $G$-tiling on a Riemannian homogeneous space $M$ to be tilings by Riemannian simplices. As evidence that this definition is natural, we prove that a large class of tilings of $M$ are MLD…