Differential Geometry Seminar: Computing shortest curves on surfaces

The task at hand is to compute a shortest loop that cannot be contracted to a point on a surface.

This is a classical problem that has been studied in different contexts, and which enjoys practical applications. In the setting of hyperbolic and convex projective geometry, I will describe a simple algorithm to compute the three shortest curves on a once-punctured torus and explain why it works. The algorithm uses an attractive interplay between algebra and geometry -- it is what Jane Gilman coined a "non-Euclidean Euclidean algorithm". This is joint work with Sepher Saryazdi.

Tagged in Differential Geometry Seminars, Seminar