Differential Geometry Seminar: Computing shortest curves on surfaces
- Date: Tue, 4 Mar 2025, 11:10 am - 12:00 pm
- Location: Engineering & Math EMG06
- Contact: Thomas Leistner
- Email: thomas.leistner@adelaide.edu.au
- Stephan Tillmann University of Sydney
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.
Speaker:
- Stephan Tillmann (University of Sydney)