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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:

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: