Related papers: Branch cuts and Riemann surfaces

We characterize which graph invariants are partition functions of an edge-coloring model over the complex numbers, in terms of the rank growth of associated `connection matrices'.

We describe some results on moduli space of logarithmic connections equipped with framings on a $n$-pointed compact Riemann surface.

We analyze the space of geometrically continuous piecewise polynomial functions or splines for quadrangular and triangular patches with arbitrary topology and general rational transition maps. To define these spaces of G 1 spline functions,…

In a previous work of the authors, a result to algorithmically compute the topology types of the level curves of an algebraic surface, is given. From this result, here we derive applications based on level curves to determine some…

Branched covers between Riemann surfaces are associated with certain combinatorial data, and Hurwitz existence problem asks whether given data satisfying those combinatorial constraints can be realized by some branched cover. We connect…

The relation between differential geometry of surfaces and some Heisenberg ferromagnet models is considered.

In classical differential geometry, a central question has been whether abstract surfaces with given geometric features can be realized as surfaces in Euclidean space. Inspired by the rich theory of embedded triply periodic minimal…

Let $Z$ be a non-compact two-dimensional manifold and $\Delta$ be a one-dimensional foliation of $Z$ such that $\partial Z$ consists of leaves of $\Delta$ and each leaf of $\Delta$ is a non-compact closed subset of $Z$. We obtain a…

Simple properties of the Gauss map characterise important classes of surfaces in $\Rq$: $R$-surfaces, the real version of plane complex curves; Lagrangean surfaces; isoclinic surfaces.

We study the variation of the Enriquez connection for higher genus polylogarithms under degenerations of Riemann surfaces with marked points, and show that this connection becomes the connection constructed by the author for degenerating…

We consider ruled surfaces with finite multiplicity. We study behaviors of the striction curves and the singularities of the ruled surfaces. We also give geometric meanings of invariants related to the ruled surfaces.

This is a survey of results on the following problem. Consider a simply connected Riemann surface spread over the Riemann sphere. How are the properties of the uniformizing function of this surface related to the geometric properties of the…

We continue to investigate the physical interpretation of the Riemann zeta function as a FZZT brane partition function associated with a matrix/gravity correspondence begun in arxiv:0708.0645. We derive the master matrix of the $(2,1)$…

In this paper we provide, first, a general symbolic algorithm for computing the symmetries of a given rational surface, based on the classical differential invariants of surfaces, i.e. Gauss curvature and mean curvature. In practice, the…

We show that the computational complexity of Riemann mappings can be bounded by the complexity needed to compute conformal mappings locally at boundary points. As a consequence we get first formally proven upper bounds for…

The study of Riemann surfaces with parametrized boundary components was initiated in conformal field theory (CFT). Motivated by general principles from Teichmueller theory, and applications to the construction of CFT from vertex operator…

We present a computational approach to general hyperelliptic Riemann surfaces in Weierstrass normal form. The surface is either given by a list of the branch points, the coefficients of the defining polynomial or a system of cuts for the…

Let $X$ be a compact Riemann surface of genus $g$ and let $x \in X$. We derive the classical presentation of $\pi_1(X,x)$ (i.e the one given by $2g$ generators $a_1,b_1, \dots, a_g,b_g$ and the relation $\prod_{i=1}^g[a_i,b_i] = 1$) from…

The topology of complex classical paths is investigated to discuss quantum tunnelling splittings in one-dimensional systems. Here the Hamiltonian is assumed to be given as polynomial functions, so the fundamental group for the Riemann…

We introduce a systematic approach to express generating functions for the enumeration of maps on surfaces of high genus in terms of a single generating function relevant to planar surfaces. Central to this work is the comparison of two…