Undergraduate Research at GANG

Undergraduate Research at GANG
Summer 2000

The Research Experience for Undergraduate (REU) program is an NSF-supported opportunity for undergraduates to participate in scientific research. The geometry- and analysis-oriented topics for Summer 2000 at the Center for Geometry, Analysis, Numerics and Graphics (GANG) include:

Curves and immersions
Three-dimensional discrete conformal geometry
Two-dimensional stochastic heat flow.

Curves and immersions
Nicholas Schmitt at GANG

Meghan Anderson
Adam Cardinal-Stakenas

The problem:

How many ways does a curve in the plane bound an immersed surface? More precisely, given an immersion

f:S¹-> R²,

of the circle into the plane, how many ways does f extend to an immersion

F:M-> R²

of a 2-manifold M?

The solution:

Illustrations and Animations:

Research Report: algorithms, proofs and examples
postscript
Software: a C++ implementation of the algorithm

This problem arises in the classification of Alexandrov-embedded genus-zero minimal surfaces in R³ with finite total curvature and horizontal catenoid ends (C. Cosin, A. Ros. preprint).

Discrete Conformal Geometry
Peter Norman at GANG

Meghan Anderson
Adam Cardinal-Stakenas

Three-Dimensional Discrete Conformal Maps: