Theta Surfaces

Connections between Theta-Graphs, Delaunay Triangulations, and Orthogonal Surfaces

Θk-graphs are geometric graphs that appear in the context of graph navigation. The shortest-path metric of these graphs is known to approximate the Euclidean complete graph up to a factor depending on the cone number k and the dimension of the space. TD-Delaunay graphs, a.k.a. triangular-distance Delaunay triangulations introduced by Chew, have been shown to be plane 2-spanners of the 2D Euclid...

Riemann Surfaces and Theta Functions MAST 661G / MAST 837J

Bundles of Generalized Theta Functions over Abelian Surfaces

We study the Verlinde bundles of generalized theta functions constructed from moduli spaces of sheaves over abelian surfaces. In degree 0, the splitting type of these bundles is expressed in terms of indecomposable semihomogeneous factors. Furthermore, Fourier-Mukai symmetries of the Verlinde bundles are found, consistently with strange duality. Along the way, a transformation formula for the t...

Moduli Spaces of Abelian Surfaces : Compactification , Degenerations , and Theta Functions (

theory of Lie groups—but many geometric questions lead to non-standard problems which go beyond, or lie on the frontiers of, standard theory. Such questions arise both in reassuringly down-to-earth topics like the existence of constant mean curvature surfaces in R, and in more esoteric ones such as the use of harmonic maps into 'buildings', which have been exploited by Gromov and Schoen to obta...

The e-Theta Hopes

The largest class of hyperstructures is the Hv-structures, introduced in 1990, which proved to have a lot of applications in mathematics and several applied sciences, as well. Hyperstructures are used in the Lie-Santilli theory focusing to the hypernumbers, called e-numbers. We present the appropriate e-hyperstuctures which are defined using any map, in the sense the derivative map, called thet...