Related papers: Moduli space intersection duality between Regge su…
We exploit the properties of the three-dimensional hyperbolic space to discuss a simplicial setting for open/closed string duality based on (random) Regge triangulations decorated with null twistorial fields. We explicitly show that the…
We show that the introduction of triangulations with variable connectivity and fluctuating egde-lengths (Random Regge Triangulations) allows for a relatively simple and direct analyisis of the modular properties of 2 dimensional simplicial…
We discuss the worldvolume description of intersecting D-branes, including the metric on the moduli space of deformations. We impose a choice of static gauge that treats all the branes on an equal footing and describes the intersection of…
A method of defining the complex structure(moduli) for dynamically triangulated(DT) surfaces with torus topology is proposed. Distribution of the moduli parameter is measured numerically and compared with the Liouville theory for the…
Differentials on Riemann surfaces correspond to translation surfaces with conical singularities, and affine transformations acting on them preserve the orders of these singularities. This viewpoint allows the moduli spaces of differentials…
In this paper we relate volumes of moduli spaces of super Riemann surfaces to integrals over the moduli space of stable Riemann surfaces $\overline{\cal M}_{g,n}$. This allows us to prove via algebraic geometry a recursion between the…
The goal of this paper is to develop some aspects of the deformation theory of piecewise flat structures on surfaces and use this theory to construct new geometric structures on the moduli space of Riemann surfaces.
The moduli spaces of compact and connected Riemann surfaces has been a central topic in modern mathematics in recent years. Thus their homological dimensions become important invariants. Motivated by the emergence mathematical counterparts…
Compactification of 6d N=(2,0) theory of type G on a punctured Riemann surface has been effectively used to understand S-dualities of 4d N=2 theories. We can further introduce branch cuts on the Riemann surface across which the worldvolume…
We define a kind of moduli space of nested surfaces and mappings, which we call a comparison moduli space. We review examples of such spaces in geometric function theory and modern Teichmueller theory, and illustrate how a wide range of…
We review and extend recent work on the application of the non-commutative geometric framework to an interpretation of the moduli space of vacua of certain deformations of N=4 super Yang-Mills theories. We present a simple worldsheet…
Using the canonical Monte Carlo simulation technique, we study a Regge calculus model on triangulated spherical surfaces. The discrete model is statistical mechanically defined with the variables $X$, $g$ and $\rho$, which denote the…
We review some of our recent work on the conformal geometry corresponding to the triangulated surfaces used in 2-dimensional simplicial quantum gravity. In particular, we discuss the regularized Liouville action associated with random Regge…
Two-dimensional conformal field theory is a powerful tool to understand the geometry of surfaces. Here, we study Liouville conformal field theory in the classical (large central charge) limit, where it encodes the geometry of the moduli…
In this paper, we are interested in flat metric structures with conical singularities on surfaces which are obtained by deforming translation surface structures. The moduli space of such flat metric structures can be viewed as some…
There is a canonical identification, due to the author, of a convex real projective structure on an orientable surface of genus g and a pair consisting of a conformal structure together with a holomorphic cubic differential on the surface.…
Cone spherical surfaces are orientable Riemannian surfaces with constant curvature one and a finite set of conical singularities. A subset of these surfaces, referred to as dihedral surfaces, is characterized by their monodromy groups,…
Our goal here is to present a detailed analysis connecting the anomalous scaling properties of 2D simplicial quantum gravity to the geometry of the moduli space M_{g,N} of genus g Riemann surfaces with N punctures. In the case of pure…
Given a smooth compact complex surface together with a holomorphic line bundle on it, using the theory of Hodge modules, we compute the twisted Hodge groups/numbers of Hilbert schemes (or Douady spaces) of points on the surface with values…
It is known that every nonorientable surface $\Sigma$ has an orientable double cover $\tilde{\Sigma}$. The covering map induces an involution on the moduli space $\tilde{\M}$ of gauge equivalence classes of flat $G$-connections on…