Related papers: Super Riemann surfaces and fatgraphs

In this work we show two results about approximating, with respect to the compact-open topology, mapping classes on surfaces of infinite-type by quasi-conformal maps, in particular we are interested in density results. The first result is…

In this paper we study the smooth moduli space of closed Riemann surfaces. This smooth moduli is an infinite cover of the usual moduli space $\mathscr{M}_g$ of closed Riemann surfaces, and is identified with the Schottky space of rank $g.$…

The Weil-Petersson and Takhtajan-Zograf metrics on the Riemann moduli spaces of complex structures for an $n$-fold punctured oriented surface of genus $g,$ in the stable range $g+2n>2,$ are shown here to have complete asymptotic expansions…

This survey paper begins with the description of the duality between arc systems and ribbon graphs embedded in a punctured surface. Then we explain how to cellularize the moduli space of curves in two different ways: using Jenkins-Strebel…

We investigate the complex of differential forms in curved, six-dimensional, $N=(1,0)$ superspace. The superconformal group acts on this complex by super-Weyl transformations. An ambi-twistor-like representation of a second conformal group…

In this paper, we study biconservative hypersurfaces in $\mathbb S^{n}$ and $\mathbb H^{n}$. Further, we obtain complete explicit classification of biconservative hypersurfaces in $4$-dimensional Riemannian space form with exactly three…

We introduce para-complex and pseudo-Riemannian geometric methods for the study of representations of surface groups in $\mathrm{SL}(2m+1,\mathbb{R})$. For $m=1$ our techniques allow to recover several known results for Hitchin…

We establish a correspondence between information geometry and gauge theory. First, we define an important class of statistical manifolds, that is normalized and satisfies a conservation field equation. Second, we prove that for a…

We study the global behavior of (weakly) stable constant mean curvature hypersurfaces in general Riemannian manifolds. By using harmonic function theory, we prove some one-end theorems which are new even for constant mean curvature…

Deformations of complex structures by finite Beltrami differentials are considered on general Riemann surfaces. Exact formulas to any fixed order are derived for the corresponding deformations of the period matrix, Green's functions, and…

We find all exceptional spin groups attached to the vertices of any exceptional spin graph on any hyperbolic Riemann surface S of genus g>1. In particular, we show that when the order r of a graph is r>2 (i.e.the genus of S must be g>3)…

We consider supersymmetric models in 5-dimensional space-time compactified on S**1/Z(2) orbifold where N=2 supersymmetry is explicitly broken down to N=1 by the orbifold projection. We find that the residual N=1 supersymmetry is broken…

When the Seiberg-Witten curve of a four-dimensional $\mathcal{N}=2$ supersymmetric gauge theory wraps a Riemann surface as a multi-sheeted cover, a topological constraint requires that in general the curve should develop ramification…

Warped products are one of the simplest families of Riemannian manifolds that can have non-trivial geometries. In this article, we characterize the geometry of hypersurface embeddings arising from warped product manifolds using the language…

Some stochastic evolutions of conformal maps can be described by SLE and may be linked to conformal field theory via stochastic differential equations and singular vectors in highest-weight modules of the Virasoro algebra. Here we discuss…

We introduce a natural generalisation of holomorphic curves to morphisms of supermanifolds, referred to as holomorphic supercurves. More precisely, supercurves are morphisms from a Riemann surface, endowed with the structure of a…

We compare the deformation theory and the analytic structure of the Seiberg-Witten moduli spaces of a K\"ahler surface to the corresponding components of the Hilbert scheme, and show that they are isomorphic. Next we show how to compute the…

In terms of appropriate extended moduli spaces, we develop a finite-dimensional construction of the self-duality and related moduli spaces over a closed Riemann surface as stratified holomorphic symplectic spaces by singular…

We describe typical degenerations of quadratic differentials thus describing ``generic cusps'' of the moduli space of meromorphic quadratic differentials with at most simple poles. The part of the boundary of the moduli space which does not…

We develop an analytic framework for Lefschetz fixed point theory and Morse theory for Hilbert complexes on stratified pseudomanifolds. We develop formulas for both global and local Lefschetz numbers and Morse, Poincar\'e polynomials as…