Related papers: Experiments with moduli of quadrilaterals

The classical theorems relating integral binary quadratic forms and ideal classes of quadratic orders have been of tremendous importance in mathematics, and many authors have given extensions of these theorems to rings other than the…

We prove a number of double-sided estimates relating discrete counterparts of several classical conformal invariants of a quadrilateral: cross-ratios, extremal lengths and random walk partition functions. The results hold true for any…

This is a review article on mirror symmetry and aspects of it related to the theory of modular forms. We describe this topic along its historical development and connect to some more recent results toward the end. The article is for…

This work is devoted to the study of integration with respect to binomial measures. We develop interpolatory quadrature rules and study their properties. Local error estimates for these rules are derived in a general framework.

We investigate gauge anomalies in the context of orbifold conformal field theories. Such anomalies manifest as failures of modular invariance in the constituents of the orbifold partition function. We review how this irregularity is…

We describe rings over which every right module is almost injective. We give a description of rings over which every simple module is a almost projective.

The purpose of these notes is to provide the details of the Jacobian ring computations carried out in [1], based on the computer algebra system Magma [2].

A ring with a test module of finite upper complete intersection dimension is complete intersection.

A new formula is obtained in algebraic topology, in terms of Betti numbers, and a new method, called the spinal method, is suggested and developed for generating quadrangulations of closed orientable surfaces. Those surfaces arise as the…

Quadric bundles on a compact Riemann surface X generalise orthogonal bundles and arise naturally in the study of the moduli space of representations of $\pi_1(X)$ in Sp(2n,R). We prove some basic results on the moduli spaces of quadric…

Double Fibonacci sequences are introduced and they are related to operations with Fibonacci modules. Generalizations and examples are also discussed.

This work builds on earlier work of the first three authors where a notion of congruence modules in higher codimension is introduced. The main new results are a criterion for detecting regularity of local rings in terms of congruence…

Pentagonal subdivision gives three families of edge-to-edge tilings of the sphere by congruent pentagons. Each family forms a two dimensional moduli. We describe the moduli in detail.

In this paper, we mainly focus on formal deformation theory of module homomorphisms. We first introduce the cohomology of module homomorphisms and study formal one-parameter deformation. We obtain some properties about obstructions. Then we…

We study the spaces of stable real and quaternionic vector bundles on a real algebraic curve. The basic relationship is established with unitary representations of an extension Z/2 by the fundamental group. By comparison with the space of…

Notions of the orthogonality and convolution orthogonality are explored with the use of the Kontorovich-Lebedev transform and its convolution. New classes of the corresponding orthogonal polynomials and functions are investigated. Integral…

Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas, and two lines. For an integral with respect to an appropriate weight function defined on any…

We characterize the generating function of the number of representations described in the title in terms of the theory of modular forms. Appealing to this characterization we obtain explicit formulas for the representation numbers as…

We introduce some compact orbifolds on which there is a certain finite group action having a simple convex polytope as the orbit space. We compute the orbifold fundamental group and homology groups of these orbifolds. We calculate the…

We prove a result which gives sufficient conditions for a conformal annulus which is a countable union of nested conformal annuli to have bounded modulus. Our theorem also gives estimates for the modulus of such an annulus and is proved…