We study the algebro-geometric aspects of Teichmüller curves parameterizing square-tiled surfaces with two applications. (a) There exist infinitely many rigid curves on the moduli space of hyperelliptic curves. They span the same extremal ray of the cone of moving curves. Their union is a Zariski dense subset. Hence they yield infinitely many rigid curves with the same properties on the moduli ...

We study bounds on the effective conductivity and elastic moduli of two-phase isotropic composites that depend on geometrical parameters that take into account up to three-point statistical information concerning the composite microstructure. We summarize existing bounds, apply a special fractional linear transformation to simplify their functional forms, and describe two approaches to improve ...

Effective electromechanical moduli of ferroelectric ceramics with fiber textures" (2005). Faculty Publications from Nebraska Center for Materials and Nanoscience. 42.

In bosonic field theories the low-energy scattering of solitons that saturate Bogomol’nyi-type bounds can be approximated as geodesic motion on the moduli space of static solutions. In this paper we consider the analogous issue within the context of supersymmetric field theories. We focus our study on a class of N = 2 non-linear sigma models in d = 2 + 1 based on an arbitrary Kähler target mani...

We investigate the one-parameter Calabi-Yau models and identify families of D5-branes which are associated to lines embedded in these manifolds. The moduli spaces are given by sets of Riemann curves, which form a web whose intersection points are described by permutation branes. We arrive at a geometric interpretation for bulk-boundary correlators as holomorphic differentials on the moduli spac...

We survey recent developments and open problems about extremal effective divisors and higher codimension cycles in moduli spaces